Given that $AB$ is parallel to $CD$, find the value(s) of the unknown(s) in the following f

Question

Given that $AB$ is parallel to $CD$, find the value(s) of the unknown(s) in the following figures, stating your reasons clearly. The figure shows a triangle $ABC$ and a parallel line $CD$. Angle $\angle BAC = y^\circ$ and $\angle ABC = x^\circ$. Outside the triangle, an exterior angle at $C$ is $112^\circ$ and $\angle BCD = 38^\circ$. Find the values of $x$ and $y$. The figure shows parallel lines $CD$ and $AB$ intersected by two transversals that meet at point $E$. Angle $\angle AEB = 100^\circ$, $\angle CEA = z^\circ$, and $\angle DEB = y^\circ$. Inside the triangle $ABE$, angle $\angle EAB = x^\circ$, and an exterior angle at $B$ is $143^\circ$. Find the values of $x$, $y$, and $z$.

Accepted Answer

(a) $x=38^\circ$, $y=74^\circ$ (b) $x=43^\circ$, $y=37^\circ$, $z=43^\circ$

Triangles

Triangles

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