Question

If the ratio of the measure of an internal angle to that of an external angle of a polygon is 3:2, then find the measure of an exterior angle.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Measure of interior angle of an `n' sided regular polygon = $\frac{(n-2){180}^{\circ }}{n}$

Measure of exterior angle of an `n' sided regular polygon = $\frac{2{\times 180}^{\circ }}{n}$

Given that ratio of internal to external angle is 3 : 2 -

$\Rightarrow$ $\left(\frac{n-2}{2}\right)$ = $\frac{3}{2}$

$\Rightarrow$ n = 5

$\therefore$ Measure of an exterior angle is ${72}^{\circ }$.