High School

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The sum of the interior angles of a pentagon is 540 degrees. The Pentagon in Washington, D.C., is named for its unusual shape, a regular pentagon. What is the measure of each angle of the pentagon?

Answer :

Final answer:

The sum of the interior angles of a pentagon is 540 degrees, and in a regular pentagon, all angles are equal. Therefore, each angle of a regular pentagon measures 108 degrees.

Explanation:

The assertion that the sum of the interior angles of a pentagon is 540 degrees is incorrect. In fact, the interior angles of any pentagon, including a regular pentagon like the one referred to in Washington, D.C., adds up to 540 degrees. The student's question pertains to a regular pentagon, which means that all its angles and sides are equal.

Therefore, to find the measure of each angle in a regular pentagon, we divide the total sum of the interior angles by the number of angles, which is five.

The sum of interior angles of a pentagon (regular or irregular) can be calculated using the formula (n-2) x 180°, where n is the number of sides. For a pentagon, n=5, thus the sum of its interior angles is (5-2) x 180° = 3 x 180° = 540°.

Consequently, each interior angle of a regular pentagon is 540° ÷ 5 = 108°.

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Rewritten by : Barada

540 divided by five is equal to 108 degrees per angle.