Question

Find the number of sides of a regular polygon if each of its interior angle is 90

Answer 1

There is a well known formula in mathematics to find number of sides of a regular polygon by knowing its interior angle.

The formula is :

Sum of total interior angles = (2n - 4)90  [where n represents number of sides]

Given each interior angle is 90.

Let the number of sides of regular polygon = n

So sum of the toal interior angles of this unkown regular polygon             = 90* number of sides

= 90n

So,

(2n - 4)90 = 90n

2n - 4 = n

2n = n + 4

n = 4

Therefore number of sides = 4

Sum of total interior angles = 90*4 = 360

Hence the given polygon is known as quadrilateral.

Hope my answer helps you.

Answer 2

Answer:

If each interior angle is 90°

Then,each exterior angle = 180°- 90°=90°(as sum of interior and exterior angle are supplementary)

Hence,The Total No.of sides of a regular polygon =Sum of exterior angle of polygon÷each side of regular polygon=360°÷90°= 4

So, the regular polygon has 4 sides and it is a square.