Question

An exterior angle and the interior angle of a regular polygon are in the ratio 2: 3 respectively. Find the
number of sides that the polygon has.​

Answer 1

Answer:

5

Step-by-step explanation:

First we will find x .

then using x, we will find the exterior angle of the polygon by using 2x (given).

we know that the number of sides in a polygon is equal to 360/exterior angle.

$2x + 3x = 180 \\ 5x = 180 \\ x = \frac{180}{5} \\ x = 36 \\ 2x = 2 \times 36 = 72 \\ n = \frac{360}{72} \\ = 5$