Question

Find the measure of one interior angle in the given polygon below. Round your answer to the nearest hundredth, if needed.
Does the polygon have to be "regular" in order for you to be able to find just one interior angle? Explain.

**Must show all work, and provide an explanation using complete sentences for credit. regular heptagon

Answer 1

Answer:

  128.57°

Step-by-step explanation:

A regular heptagon is a 7-sided polygon whose 7 interior angles all have the same measure. The measure of each of them in degrees can be computed from the formula

  interior angle measure = 180(n-2)/n . . . where n = 7 is the number of sides

  interior angle measure = 180(5/7) = 128 4/7 ≈ 128.57

The measure of one interior angle of a regular heptagon is about 128.57°.

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The polygon does not have to be regular to find an interior angle. It needs to be of such a nature that the interior angles are known from the description of the polygon. For example, an isosceles right triangle is not a regular polygon, but you know that the measure of one acute angle is 45°.