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Which of the following are true of a regular pentagon?

a) Each angle measure is 108°.
b) The angle sum is 720º.
c) It has six sides.
d) It is equilateral.

User Gaffcz
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1 Answer

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Final answer:

A regular pentagon has five equal-length sides and each angle is 108°. The sum of the angles of a pentagon is 540°, and since a regular pentagon has equal-length sides, it is equilateral. A figure with six sides is a hexagon, not a pentagon.

Step-by-step explanation:

The characteristics of a regular pentagon include that it has five equal-length sides and five equal angles. To find the measure of each interior angle in a regular polygon, you can use the formula: (n - 2) × 180° / n, where n is the number of sides. Applying this formula to a pentagon (n = 5), we get (5 - 2) × 180° / 5 = 540° / 5 = 108° for each angle. Thus, option a) each angle measure is 108° is correct.

Additionally, the sum of all the interior angles of a polygon can be found using the formula (n - 2) × 180°. For a pentagon, this would be (5 - 2) × 180° = 3 × 180° = 540°, not 720° as option b) states. Therefore, option b) the angle sum is 720° is incorrect for a pentagon. A regular pentagon is also equilateral, meaning all sides are the same length, which corresponds with option d).

Option c) mentioning a figure with six sides is describing a hexagon, not a pentagon. Therefore, it is not a correct characteristic of a regular pentagon.

User Yellen
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