Question

If the ratio between the interior and exterior angles of a regular polygon is 14 : 1, then the polygon has ___ sides.

• A. 20
• B. 30
• C. 40
• D. 60

Answer 1

The correct option is B 30

Let the interior angle (i) = 14x and the exterior angle (e) = x

We know, i + e = ${180}^{\circ }$

14x + x = ${180}^{\circ }$

15x = ${180}^{\circ }$

x = ${12}^{\circ }$

$\therefore e={12}^{\circ }$

$n=\frac{{360}^{\circ }}{e^{\circ }}$

$\frac{{360}^{\circ }}{{12}^{\circ }}$

= 30

Ans (A)