Question

the ratio of an interior angle to an exterior angle of a regular polygon is 3:2 what is the number of sides of the polygon?

Answer 1

7x + 2x = 180

=> x = 20

Exterior angle = 40 degrees

now (exterior angle) = 360/(no. of sides)

solving, you will get no. of sides = 9.

I HOPE ITS HELPFUL

Answer 2

ⓢⓞⓛⓤⓣⓘⓞⓝ ⤵️

sum of interior and exterior angle of a regular polygon is 180°

interior angle=3x

exterior angle=2x

According to the question,

3x+2x=180

or,5x=180

or,x=180/5(dividing both sides by 5)

or,x=36(solution)

interior angle of the regular polygon=108°

exterior angle of the regular polygon=72°

to find the number of sides we used the formula of sides of regular polygon

the formula is given,

360°/measure of each exterior angle

si the number of sides =360°/72°=5

number of diagonal=n( n-3)/2

=5(5-3)/2

=10/2=5

regular polygon is a type of polygon whose all sides and all angles are equal.