Question

In a regular polygon if the ratio of the interior and exterior angles is 3:2 then the interior angle of the polygon is ___

• A. 70${}^{\circ }$
• B. 36${}^{\circ }$
• C. 108${}^{\circ }$
• D. 100${}^{\circ }$

Answer 1

The correct option is C

108${}^{\circ }$

Given: The polygon is regular and the ratio of the interior and exterior angles = 3:2

In a regular polygon , the interior angle + the exterior angle = ${180}^{\circ }$

Let the interior angle = 3$x$ and the exterior angle = 2$x$

Hence 3$x$ + 2$x$ = ${180}^{\circ }$

5$x$ = ${180}^{\circ }$

$x$ = ${36}^{\circ }$

Hence the measure of the interior angle = 3(36) = ${108}^{\circ }$