Question

In a regular polygon, the ratio of the interior angle to the corresponding exterior angle is 14 : 4. How many sides does this polygon have ?

• A. 10
• B. 3
• C. 9
• D. 7

Answer 1

The correct option is C

9

Given : Ratio of interior angle to the corresponding exterior angle = 14 : 4

We know that sum of interior angle and the corresponding exterior angle is equal to ${180}^{\circ }$.

We need to divide ${180}^{\circ }$ in 14 + 4 = 18 parts.

Measure of each part = $\frac{{180}^{\circ }}{18}={10}^{\circ }$

$\therefore$ Measure of exterior angle
= 4 $\times$ Measure of each part = ${40}^{\circ }$

We know that sum of all the exterior angles of a polygon is ${360}^{\circ }$.

Number of sides of the polygon

= $\frac{{360}^{\circ }}{Exteriorangle}$ = $\frac{{360}^{\circ }}{{40}^{\circ }}$ = 9