Question

The ratio between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.

Answer 1

Answer:

12

Step-by-step explanation:

Given :  The ratio between exterior angle and interior angle of a regular polygon is 1:5.

To Find : Find the number of sides of the polygon

Solution:

The sum of  one exterior angle and one interior angle is 180°  since they form a linear pair.

Let the ratio be x

So, exterior angle = x

Interior angle = 5x

So,$x+5x=180^{\circ}$

$6x=180^{\circ}$

$x=30$

So, exterior angle is 30°

Let n be the number of sides

Formula : $n \times \text{exterior angle} = 360 ^{\circ}$

So, $n \times 30= 360 ^{\circ}$

$n =12$

Hence the number of sides of the polygon is 12.