Question

If the ratio between the exterior angle and interior angle of a regular polygon is 2: 3, then the polygon is ___.

• A. triangle
• B. hexagon
• C. decagon
• D. pentagon

Answer 1

The correct option is D

pentagon

It is given that the polygon is regular. So all the sides and angles of the polygon are equal.

Let exterior angle = 2x

$\Rightarrow$ Interior angle = 3x° (given)

In a polygon, the sum of an interior angle and its respective exterior angle is 180°

$\Rightarrow$ 3x + 2x = 180°

$\Rightarrow$ 5x = 180°

$\Rightarrow$ x = 36°

$\therefore$ exterior angle = 2$\times$36°

= 72${}^{\circ }$

$\because$ Sum of exterior angles of any polygon = 360${}^{\circ }$

$\Rightarrow$ n $\times$ exterior angle = 360${}^{\circ }$ (where, n= Number of sides)

$\Rightarrow$ n =$\frac{360°}{\text{exterior angle}}$

= $\frac{360°}{72°}$

= 5

$\because$ The number of sides in given polygon is 5, so the given polygon is pentagon.