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:

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

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.

Answer 2

Answer:

The polygon is a Regular Nonagon . It’ll have 9 equal sides.

Since, interior angle + exterior angle of any polygon ,at one vertex = 180° & the ratio of these angles = 7:2

=> 7x + 2x = 180

=> 9x = 180

=> x = 20

=> 7x = 140° & 2x = 40°

=> Here interior angle has to be 140° as interior angle of any regular polygon can not be less than 60°

Now, we know the formula of each interior angle of a regular polygon = (n-2)180 / n , (where n is the number of sides of the polygon)

=> (n-2)*180 / n = 140

=> 180n - 140n = 360

=> 40n = 360

=> n = 9

So, the regular polygon has 9 equal sides.