Question

The sum of angles of regular polygon is 5670°. Find the number of sides of the polygon​

Answer 1

Sum of angles= 5670°

We know that

(no. of sides - 2) * 180 = sum of all angles

let the no. of sides be x

(x-2) * 180 = 5670

(x-2) = 5670/180

x-2 = 31.5

x = 31.5 + 2

x = 33.5

Answer 2

Given:

Sum of angles of a regular polygon = 5760º

To Find:

Number of sides of the polygon

Concept Used

Sum of angles of a polygon = (n - 2) x 180 where n is the number of sides.

Steps

Sum of angles = (n - 2) x 180

(n - 2) x 180 = 5760

n - 2 = 5760 ÷ 180

n - 2 = 32

n = 32 + 2

n = 34

The polygon has 34 sides.