Question

How to find the number of sides of a polygon when given the interior angle sum

Answer 1

Given:

Sum of interior angle

To find:

Number of sides of a polygon

Solution:

Using sum of interior angles formula:

$S=(n-2) \times 180^{\circ}$

where "S" is the sum of interior angels and "n" is the number of sides of a polygon.

Divide by 180° on both sides.

$\frac{S}{180^{\circ}}=\frac{(n-2) \times 180^{\circ}}{180^{\circ}}$

Cancel common factor 180°.

$\frac{S}{180^{\circ}}=n-2$

Add 2 on both sides.

$\frac{S}{180^{\circ}}+2=n-2+2$

$\frac{S}{180^{\circ}}+2=n$

Switch the sides.

$n=\frac{sum}{180^{\circ}}+2$

Therefore number of sides of a polygon is $n=\frac{sum}{180^{\circ}}+2$.