The ratio of the exterior angle to the interior angle of a regular polygon is 1:11. How many sides has the polygon?

A. 30
B. 24
C. 18
D. 12

Correct Answer: Option B

B. 24

Explanation

Let a represent an interior angle; e represent an exterior angle. A section of the polygon is down in the diagram.

e/a = 1/11 given

a = 11e

a + e = 180° (angles on a straight line)

11e + e = 180°

12e = 180°

e = 180°/12

= 15°

Hence, number of sides

= 360°/14°

= 24