Question

In a regular polygon, the ratio of the inner and outer 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 : The ratio of interior angle to exterior angle = 14 : 4

We know, Sum of interior and exterior angle = ${180}^{\circ }$

So, 14x + 4x = 180

$\Rightarrow$ 18x = 180

$\Rightarrow$ x = 10

$\therefore$ Exterior angle = 4x = ${40}^{\circ }$

Number of Sides of the Polygon = $\frac{360}{Exteriorangle}$ = $\frac{360}{40}$ = 9