Question

The ratio of an interior angle to an exterior angle of a regular polygon is 5 : 2. What is the number of sides of the polygon ?​

Answer 1

Answer:

Step-by-step explanation:

the interior angle of a regular polygon is equal to 180 - 360 / n, where n is the number of sides. the ratio of the interior angle of the polygon to the exterior angle of the polygon is equual to 5/2. thie means that (180 - 360 / n) / (360 / n) is equal to 5 / 2.

Answer 2

Step-by-step explanation:

$\huge\underline\bold {Answer:}$

Interior angle of polygon of n sides = (n – 2) × 180°/n

Exterior angle of a polygon of n sides = 360°/n

Given, (n – 2) × 180°/n : 360°/n = 5 : 2

=> (n – 2) × 180°/n × 360°/n = 5/2

=> (n – 2)/2 = 5/2

=> 2(n – 2) = 10

=> 2n – 4 = 10

=> 2n = 14

=> n = 7.

Therefore number of sides of the polygon is 7.