Question

In a regular polygon if the ratio of exterior angle to its interior angle is 2 : 7, then the polygon has ___ sides.

• A. 6
• B. 8
• C. 9
• D. 10

Answer 1

The correct option is C

9

Let each exterior angle (e°) = 2x and each interior angle (i°) = 7x.

We know, interior angle (i°) + exterior angle (e°) = 180°

7x° + 2x° = 180°

9x° = 180°

x = 20°

exterior angle (e°) = 2x = 40°

Number of sides (n) = $\frac{360°}{e°}$

Number of sides (n) = $\frac{360°}{40°}$

Number of sides (n) = 9