In the figure below, $ABC$ is a triangle enclosed by straight lines $MN$, $PQ$ and $RS$, whe

Question

In the figure below, $ABC$ is a triangle enclosed by straight lines $MN$, $PQ$ and $RS$, where angles such as angle $CAN$, angle $ABR$ and angle $ACS$ are known as exterior angles of triangle $ABC$. Using this figure, show that angle $CAN = $ angle $ABC + $ angle $ACB$, i.e., the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle (remote interior angles), which is known as the Exterior Angle Theorem. Apply the Exterior Angle Theorem on the other two exterior angles, angle $ABR$ and angle $ACS$, by stating the relationship between the exterior angles and corresponding interior angles.

Accepted Answer

(a) $\angle CAN=\angle ABC+\angle ACB$ (b) $\angle ABR=\angle BAC+\angle ACB$, $\angle ACS=\angle BAC+\angle ABC$

Triangles

Triangles

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