Question

find the number of sides of a polygon, if the ratio btw an exterior angle and interior angle of a regular polygon is 1:5 ​

Answer 1

Answer: 12 Sides

Step-by-step explanation:

Ratio btw the exterior and the interior angle of a regular polygon is 1:5

Let the common multiple be 'k'

Therefore , Measure of exterior angle = (1k)°

And , the measure of an interior angle = (5k)°

We know , the sum of measures of interior and exterior angle of a regular polygon is 180°

Therefore ,

(1k)°+(5k)°= 180°

(6k)° = 180°

k = 180°/6°

therefore , k = 30°

therefore the measure of exterior angle = (1k)° = 30°

and , the measure of interior angle = (5k)° = 150°

We know ,

No.of sides of a regular polygon = 360°/measure of an

exterior angle

= 360°/30°

= 12

Therefore the number of sides of the given polygon is 12.