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What is the Measure of an Interior Angle of a Regular Pentagon?

When you’re trying to figure out how to make a pentagon, one of the first questions you may have is: what is the measure of an interior angle? The answer is 180deg/n. That’s right, a regular pentagon has 108 interior angles. The opposite, the exterior angles, are a fraction of the interior angles and are equal to 360deg/n.

Inside the pentagon, the interior angles are formed by the adjacent pairs of sides. The interior angles with a common side are called adjacent interior angles. A regular pentagon has five sides, so the interior angles are equal in number. The exterior angles, on the other hand, are formed by the extended sides of the pentagon. In addition to interior angles, regular pentagons have equal exterior angles and interior angles.

To figure out the interior angles of a regular pentagon, divide the pentagon into triangles. Each triangle has three angles, so the sum of these angles is 180 degrees. The central angle, in contrast, is 72 degrees. If the interior angles of a regular pentagon are the same, they will all be the same measure. Hence, the sum of interior angles of a pentagon is equal to 540 degrees.

For example, if a regular pentagon has five congruent sides, then the measure of each side’s interior angle is 180n. Each side should connect to the first segment. The last segment of the regular pentagon should end at the starting point of the first segment. Using the Polygon Interior Angles Sum Theorem, you can write down an equation that answers this question.

Regular polygons also have exterior angles. These are not the same as the interior angle. When you want to extend a side of a polygon, you need to add the interior angle to the exterior angle. If the two angles are adjacent, the measure of each exterior angle is 360deg. The other way to move around a polygon is to rotate it in a full circle.



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