A Math

A Math (IGCSE)

E Math

E Math (IGCSE)

H1 Math

H2 Math

IB AA HL Math

IB AA SL Math

IB AI HL Math

IB AI SL Math

IP Math

N(A) A Math

N(A) E Math

PSLE

<p>In the figure below, $MON$ is a straight line. $OP$ is a random ray with endpoint $O$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">The rays $OQ_1$ and $OR_1$ are the bisectors of the angle $MOP$ and angle $NOP$, respectively. Find the size of angle $Q_1OR_1$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/06/Extra-Practice-Q9-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1ROS1pLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.Dw3_ckcIWP8qL02inUEND3JNg6cJvXgu9p1eERsF1zI" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph">By extending the figure in (i), the rays $OQ_2$ and $OR_2$ are the bisectors of angle $Q_1OP$ and angle $R_1OP$, respectively. Find the size of angle $Q_2OR_2$ and state a pattern or assumption you find about angle $Q_2OR_2$ and angle $Q_nOR_n$ where $n &gt; 2$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/06/Extra-Practice-Q9-ii-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1ROS1paS1kaWFncmFtLTEucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.g11iTOS8iN7ymK0YrpFZ8pg4-p1zDsBPBgBSrcN7nAU" alt="List item image" class="aligncenter custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph"><strong>By extending the figure in (ii)</strong>, the rays $OQ_3$ and $OR_3$ are the bisectors of angle $Q_2OP$ and angle $R_2OP$, respectively. Find the size of angle $Q_3OR_3$ and test whether your assumption also holds for angle $Q_3OR_3$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/06/Extra-Practice-Q9-iii-diagram-624x283.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1ROS1paWktZGlhZ3JhbS02MjR4MjgzLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.TvrFEczXQ_GiJIiUvvM8nSHJJOjwzCGbFHyfAcIxaFs" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li><li><div class="list-item-paragraph"><strong>Based on the pattern you find</strong>, complete the following table, where the <strong>4th</strong> and <strong>5th</strong> patterns are given.</div></li></ol>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Pattern Number, $n$</th><th style="text-align: left; --cell-justify: flex-start">Size of angle $Q_nOR_n$</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">1</td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: left; --cell-justify: flex-start">2</td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: left; --cell-justify: flex-start">3</td><td style="text-align: left; --cell-justify: flex-start"></td></tr><tr><td style="text-align: left; --cell-justify: flex-start">4</td><td style="text-align: left; --cell-justify: flex-start">$11.25^\circ = 180^\circ \times (\frac{1}{2})^4$</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">5</td><td style="text-align: left; --cell-justify: flex-start">$5.625^\circ = 180^\circ \times (\frac{1}{2})^5$</td></tr><tr><td style="text-align: left; --cell-justify: flex-start">...</td><td style="text-align: left; --cell-justify: flex-start">...</td></tr></tbody></table></div></div>
<ol class="i-list" start="5"><li><div class="list-item-paragraph"><strong>Based on your previous answers</strong>, find the general term of size of $Q_nOR_n$ in terms of $n$, where $OQ_n$, $OR_n$ are the bisectors of angle $Q_{n-1}OP$ and angle $R_{n-1}OP$ respectively and $n$ is an integer that is greater than 3.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/06/Extra-Practice-Q9-v-diagram-624x266.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNi9FeHRyYS1QcmFjdGljZS1ROS12LWRpYWdyYW0tNjI0eDI2Ni5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzUxLCJleHAiOjE3OTI2NjMwNTF9.oOCpSkgS2gYWR8Kb2jH0q5r8urzOfl6fXKaFh3G0Vfg" alt="List item image" class="aligncenter custom-width" style="max-width: min(350px, 100%); height: auto;" /></div></li></ol>

In the figure below, $MON$ is a straight line. $OP$ is a random ray with endpoint $O$.

The rays $OQ_1$ and $OR_1$ are the bisectors of the angle $MOP$ and angle $NOP$, respectively. Find the size of angle $Q_1OR_1$.

By extending the figure in (i), the rays $OQ_2$ and $OR_2$ are the bisectors of angle $Q_1OP$ and angle $R_1OP$, respectively. Find the size of angle $Q_2OR_2$ and state a pattern or assumption you find about angle $Q_2OR_2$ and angle $Q_nOR_n$ where $n > 2$.

General Term of a Sequence

Rules of Sequences

Angles

Number Patterns

Basic Geometry

<p>Given that $AOB$
 and $COD$
 are straight lines. Find the value(s) of the unknown(s) in each of the figures below, stating your reasons clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-13-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMy1pLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.1Dhxjnj9iqB9Q40LMaxshuXYvilFK1_BrL19EilAWrs" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-13-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMy1paS1kaWFncmFtLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.asY_-xcKOPPD_vzSnK4sA-CU8T8i3jRhLTpM92dWYvE" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

Given that $AOB$
 and $COD$
 are straight lines. Find the value(s) of the unknown(s) in each of the figures below, stating your reasons clearly.

<p>Find the value of $x$
 in each of the figures below, stating your reasons clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-12-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1pLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.agufUD8FsdBPV75T2UvTJYEuWBPtgztRppdgjpw9wOE" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-12-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMi1paS1kaWFncmFtLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.X3xcRSurh8fu5TvMJRkZFvW8uInA-wgA7VdpD9chXyw" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

Find the value of $x$
 in each of the figures below, stating your reasons clearly.

<p>Given that $ABC$
 is a straight line. Find the value(s) of the unknown(s) in each of the figures below, stating your reasons clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-11-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMS1pLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.gUO-yo14JMSg52QVP_7D50OVtLDTndVhuSKmKzSBVGQ" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-11-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xMS1paS1kaWFncmFtLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.ydWFfH4mlg8VbfJ6qUrvADHCvf9P_DAgW5s6lTBHwVo" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

Given that $ABC$
 is a straight line. Find the value(s) of the unknown(s) in each of the figures below, stating your reasons clearly.

<p>Given that $AOB$ and $COD$ are straight lines. Find the values of $x$ and $y$ in each of the figures below, stating your reasons clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-7-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi03LWktZGlhZ3JhbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzUxLCJleHAiOjE3OTI2NjMwNTF9.d0dhGgqJsG4pB-Vc8Qmy4WjvleDqiGAgQapK_Cqb7dY" alt="List item image" class="alignleft custom-width" style="max-width: min(250px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-7-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi03LWlpLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.LEUNi0EbLSJwZG136JHIH-ao2Io1OH0Qr_1pp_d4LiQ" alt="List item image" class="alignleft custom-width" style="max-width: min(251px, 100%); height: auto;" /></div></li></ol>

Given that $AOB$ and $COD$ are straight lines. Find the values of $x$ and $y$ in each of the figures below, stating your reasons clearly.

<p>Find the value of $x$
 in each of the figures below, stating your reason clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-6-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi02LWktZGlhZ3JhbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzUxLCJleHAiOjE3OTI2NjMwNTF9.KsZTwCMN-iZVP_qjMCbhhMVKaXsYYw2C9513LZLecgg" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-6-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi02LWlpLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.0mrJCzZt17s-JY8mtdLnc0IqoxEhp-aZjKGV9uYtnag" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

Find the value of $x$
 in each of the figures below, stating your reason clearly.

<p>Given that $ABC$
 is a straight line. Find the value of $x$
 in each of the figures below, stating your reason clearly.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-5-i-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi01LWktZGlhZ3JhbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzUxLCJleHAiOjE3OTI2NjMwNTF9.uS1IBnOkW3gG_q85XVeEraNuG_fF5WqmUmH0TmH20xU" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-5-ii-diagram.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi01LWlpLWRpYWdyYW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.ZV2LgW7PiB3u3dGFQ7P1IFEbhCjmtk-Nfp_MYFDpHIs" alt="List item image" class="alignleft custom-width" style="max-width: min(300px, 100%); height: auto;" /></div></li></ol>

Given that $ABC$
 is a straight line. Find the value of $x$
 in each of the figures below, stating your reason clearly.

<p>Find the supplementary angle of each of the following angles.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">53°</span></div></li><li><div class="list-item-content"><span class="list-item-text">30°</span></div></li><li><div class="list-item-content"><span class="list-item-text">150°</span></div></li><li><div class="list-item-content"><span class="list-item-text">120°</span></div></li><li><div class="list-item-content"><span class="list-item-text">108°</span></div></li><li><div class="list-item-content"><span class="list-item-text">135°</span></div></li></ol>

Find the supplementary angle of each of the following angles.

<p>Find the complementary angle of each of the following angles.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">1°</span></div></li><li><div class="list-item-content"><span class="list-item-text">21°</span></div></li><li><div class="list-item-content"><span class="list-item-text">30°</span></div></li><li><div class="list-item-content"><span class="list-item-text">60°</span></div></li><li><div class="list-item-content"><span class="list-item-text">37°</span></div></li><li><div class="list-item-content"><span class="list-item-text">45°</span></div></li></ol>

Find the complementary angle of each of the following angles.

<p>Classify each of the following angles as an acute, right, obtuse, straight or reflex angle.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">89°</span></div></li><li><div class="list-item-content"><span class="list-item-text">23°</span></div></li><li><div class="list-item-content"><span class="list-item-text">135°</span></div></li><li><div class="list-item-content"><span class="list-item-text">239°</span></div></li><li><div class="list-item-content"><span class="list-item-text">90°</span></div></li><li><div class="list-item-content"><span class="list-item-text">180°</span></div></li></ol>

Classify each of the following angles as an acute, right, obtuse, straight or reflex angle.

<p>Classify each of the following angles as an acute, right, obtuse, straight or reflex angle.</p>
<ol class="abc-list"><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-a-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWEtZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.dXQdTsxADn0_hAHXlKDewJnJgzmNZHVzQcVqIKQ6iXg" alt="List item image" class="alignleft custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-b-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWItZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.AwjF4BUIWpGzfS_9GP_v1VrgrOm-14XQdwHmPuDXV9A" alt="List item image" class="alignleft custom-width" style="max-width: min(199px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-c-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWMtZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.Yj0lYqiyFBy7KefiX-TGplaggBTa9y0ooRYnI_0qNiI" alt="List item image" class="alignleft custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-d-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWQtZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.vjvQgYgPv6Zdrmuugy9c_Nzugkb2ppKuk2QRR5u736o" alt="List item image" class="alignleft custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-e-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWUtZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.hxZ0zjz-Od72YxZRySZUyFFRCQkoojRny5D5hwDi1OI" alt="List item image" class="alignleft custom-width" style="max-width: min(199px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: left;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/migrated/2024/05/Question-1-f-diagram-1.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvbWlncmF0ZWQvMjAyNC8wNS9RdWVzdGlvbi0xLWYtZGlhZ3JhbS0xLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI2NjI3NTEsImV4cCI6MTc5MjY2MzA1MX0.oCIZEbUzZ-0ixtYHpOHR5kWA7NX1KUtIWWuJQ-aqE0g" alt="List item image" class="alignleft custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li></ol>

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In diagram below, $BF$ is parallel to $ED$. Angle $FBC=45{}^\circ $ and angle $CDE=118{}^\circ $.<br>Find the values of $a$ and $b$ in the figure below, stating your reasons clearly.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764059886107-e8caz6kexrl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNTk4ODYxMDctZThjYXo2a2V4cmwucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.Kop8-zElNBY94gWo18eRbA7Q4_b7MQGNNd4q5qFfQY4" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Angles Formed by Two Parallel Lines and a Transversal

Geometry: Solving for $a$ and $b$

<p>In the figure above,$AEFG$ and $CFD$ are straight lines and $AB//CD$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Angle $ECF=50{}^\circ $ and angle $DFG=20{}^\circ $. Find</p><ol class="abc-list"><li><div class="list-item-paragraph">$\angle EFC$</div></li><li><div class="list-item-paragraph">$\angle AEC$</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764050447074-ucp73ji72i.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNTA0NDcwNzQtdWNwNzNqaTcyaS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjYyNzUxLCJleHAiOjE3OTI2NjMwNTF9._t9mYBethtEqbMnlROgEVZFr_VvHcGz8EhqdXRf0gNM" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the figure above,$AEFG$ and $CFD$ are straight lines and $AB//CD$.

Angles in Parallel Lines and Transversals

<p>In the following diagram (not drawn to scale), $ABC$ is a triangle and $AB$ is parallel to $DEFG$.  Angle $DEC=120{}^\circ $ and angle $BFG=75{}^\circ $.<br>Stating your reasons clearly in your workings,</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find </p><ol class="abc-list"><li><div class="list-item-paragraph">$\angle AEG$</div></li><li><div class="list-item-paragraph">$\angle ABC$</div></li><li><div class="list-item-paragraph">$\angle CAB$</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764050067459-5gi2y0pj19m.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNTAwNjc0NTktNWdpMnkwcGoxOW0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.2wAZX_Z9H5jFLSKvOOB2tjlJzZXjwr_Q463-f2Tqgp4" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the following diagram (not drawn to scale), $ABC$ is a triangle and $AB$ is parallel to $DEFG$.  Angle $DEC=120{}^\circ $ and angle $BFG=75{}^\circ $.
Stating your reasons clearly in your workings,

Angle Relationships in Triangles and Transversals

<p>In the diagram given below, $PQ$ and $TU$ are parallel and $WYM$ and $NXM$ are straight lines. Stating your reasons clearly, determine the values of $a$, $b$ and $c$.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764049399886-17ar7qptpdt.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNDkzOTk4ODYtMTdhcjdxcHRwZHQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.DuFJdU33HGCcBcWdB4l0Db1W4u-8ViZuD-OHFQIDRAA" style="max-width: min(400px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

In the diagram given below, $PQ$ and $TU$ are parallel and $WYM$ and $NXM$ are straight lines. Stating your reasons clearly, determine the values of $a$, $b$ and $c$.

Triangle Angle Sum and Exterior Angles

Angles in Parallel Lines with Transversals

Polygons

<p>Find the values of $p$ and of $q$ in the diagram below, giving the reason for your answers.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764046483334-6zuu57aegr6.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNDY0ODMzMzQtNnp1dTU3YWVncjYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.2lLxnS2frlEo5QeruBNQY_3iLMQeoTqw6Q4QyuAv3bw" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

Find the values of $p$ and of $q$ in the diagram below, giving the reason for your answers.

Finding Unknown Angles Using Perpendicular Lines

<p>Given&nbsp;$BOD$ is a straight line, $\angle AOD=75{}^\circ ,\mathrm{ }\angle AOB=5m{}^\circ ,\mathrm{ }\angle BOC=n{}^\circ $ and $\angle COD=3m{}^\circ $, find the values of $m$ and of $n$, stating your reason clearly.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764046248106-edl8s0be2xj.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNDYyNDgxMDYtZWRsOHMwYmUyeGoucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.nJz1nkynxACJb3YtOuq5uYKhaFIq_lZEzaIjiEBSdOw" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

Given $BOD$ is a straight line, $\angle AOD=75{}^\circ ,\mathrm{ }\angle AOB=5m{}^\circ ,\mathrm{ }\angle BOC=n{}^\circ $ and $\angle COD=3m{}^\circ $, find the values of $m$ and of $n$, stating your reason clearly.

Solving Angles Around a Point Using Algebra

<p>In the diagram below, $ABC$ is a straight line.  Form an equation in $x$ and, hence, find $\angle DBE$, stating your reason clearly.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764045991380-1wb6ln7utf8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNDU5OTEzODAtMXdiNmxuN3V0ZjgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.Be63i95f7yIdsNM56i7XplxFnDKo-k39-kaFTotpTJU" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

In the diagram below, $ABC$ is a straight line.  Form an equation in $x$ and, hence, find $\angle DBE$, stating your reason clearly.

Angles on a Straight Line with Algebraic Expressions

<p>$AOB$ and $COD$ are straight lines.  Find the value of $x$ in the figure, stating your reason clearly.</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1764045720387-lvcu3ytz8ur.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjQwNDU3MjAzODctbHZjdTN5dHo4dXIucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.6VolxoeEzHOBjRebf-MYhqWvgaQ5XJvzqdXGzq-wJxw" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

$AOB$ and $COD$ are straight lines.  Find the value of $x$ in the figure, stating your reason clearly.

Angles Formed by Intersecting Straight Lines

<p>The diagram shows two straight lines, $AB$ and $CD$, intersecting at $O$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>$\angle DOB=39{}^\circ $ and $\angle COE=81{}^\circ $.<br></p><p>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">$\angle AOC$,</div></li><li><div class="list-item-paragraph">the value of $x$,</div></li></ol><p>stating your reason clearly.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1763989304807-qupjsqkzdsa.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjM5ODkzMDQ4MDctcXVwanNxa3pkc2EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY2Mjc1MSwiZXhwIjoxNzkyNjYzMDUxfQ.y1iE9TtI52pwe9fMNa4CyTGTjo0tMrVPQj7dg1q79mA" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram shows two straight lines, $AB$ and $CD$, intersecting at $O$.

Math Question Bank