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The sum of the measure of the interior angles of a polygon is 1080°. What polygon is it?

A polygon that has all sides of the same length and all angles of the same measure is called a regular polygon. The angle that lies inside a polygon is called the interior angles.

Answer: It is a regular octagon.

Let’s see the solution step by step.

Explanation:

We have to solve this for a number of sides of the polygon(p).

The formula for the sum of interior angles, of a regular polygon with p sides is,

Sum = 180(p – 2).

Put, sum of interior angles = 1080° (Given)

1080° = 180(p – 2).

1080° / 180 = (p – 2).

6 = (p – 2).

p = 6 + 2

p = 8

Hence, the polygon that has 8 sides is called an octagon.

The figure of a regular octagon is given below:

Thus, it is a regular octagon that has the sum of the measure of the interior angles is 1080°.

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