Question

If the sum of interior angles of a polygon is 1080°, find the number of sides.​

Answer 1

The polygon with an interior angle

sum of 1080° is an octagon, or

polygon with 8 sides.

We are given that the interior angle

sum of our polygon is 1080°. We also

know that the sum of the interior

angle of any polygon with "n" sides is

given by the formula (n - 2) × 180°.

Therefore, to determine the number

of sides that our polygon has, we set

this formula equal to 1080°, and solve

for "n".

• (n - 2) × 180° = 1080°

Divide both sides of the equation by

180°.

• n - 2 = 6

Add 2 to both sides of the equation.

• n = 8

We get that our polygon has 8 sides,

and the name of a polygon with 8 sides

is an octagon. Therefore, the polygon

that has an interior angle sum of 1080°

is an octagon, or an 8 sided polygon.