The interior angle of a regular n-gon is given by which expression?

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Multiple Choice

The interior angle of a regular n-gon is given by which expression?

The main idea is that the total of all interior angles in any n-gon equals (n−2)×180 degrees. In a regular polygon, every interior angle is the same, so each angle is that total divided by n. Doing that division gives [(n−2)×180]/n, which is the measure of one interior angle. The expression with 360 in the numerator relates to exterior angles, whose sum is 360 degrees, not the interior angles. Swapping the numerator and denominator would give a value that doesn’t match the actual angle size. So the correct form is [(n−2)×180]/n.

The main idea is that the total of all interior angles in any n-gon equals (n−2)×180 degrees. In a regular polygon, every interior angle is the same, so each angle is that total divided by n. Doing that division gives [(n−2)×180]/n, which is the measure of one interior angle.

The expression with 360 in the numerator relates to exterior angles, whose sum is 360 degrees, not the interior angles. Swapping the numerator and denominator would give a value that doesn’t match the actual angle size. So the correct form is [(n−2)×180]/n.

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