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The sum of the measure of the interior angles of a polygon is 1080°. What polygon is it?
Answer: It is a regular octagon.
Let's see the solution step by step.
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°.