Question

If the ratio of the exterior angle and interior angle of a regular polygon is 2: 3, the number of sides of the polygon is

• A. 7
• B. 6
• C. 5
• D. 4

Answer 1

The correct option is C

5

It is given that the polygon is regular.

Let exterior angle = 2x°

Interior angle = 3x° (given)

In a regular polygon,

interior angle + exterior angle = 180°

3x + 2x = 180°

5x = 180°

x = 36°

$\therefore$ Exterior angle = $2\times 36°=72°$

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

= $\frac{360°}{72°}$

= 5

Hence (C)