Question

In a regular polygon, if the ratio of the interior and exterior angle is 3 : 1, then find the difference between the interior and exterior angle of the polygon.

• A. 70${}^{\circ }$
• B. 45${}^{\circ }$
• C. 90${}^{\circ }$
• D. 135${}^{\circ }$

Answer 1

The correct option is C

90${}^{\circ }$

Given: The polygon is regular and the ratio of interior and exterior angle = 3:1

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

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

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

4$x$ = ${180}^{\circ }$

$x$ = ${45}^{\circ }$

Hence the measure of the exterior angle = ${45}^{\circ }$

Measure of the interior angle = 45(3) = ${135}^{\circ }$

Hence the difference = ${135}^{\circ }$ - ${45}^{\circ }$ = ${90}^{\circ }$