Question

The interior angle at a vertex of a pentagon measures ${115}^{\circ }$, determine the value of the exterior angle at the same vertex.

• A. ${75}^{\circ }$
• B. ${65}^{\circ }$
• C. ${85}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${65}^{\circ }$

Given: Interior angle $={115}^{\circ }$

We know that, the interior and the exterior angle at a vertex form a linear pair.

A linear pair means the sum of those two angles is ${180}^{\circ }$.

Interior angle $+$ Exterior angle $={180}^{\circ }$

${115}^{\circ }+$ Exterior angle $={180}^{\circ }$

Exterior angle $={180}^{\circ }-{115}^{\circ }={65}^{\circ }$