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Chapter 3: Q37. (page 115)

If the measures of each interior angle of a regular polygon is 108, then the polygon is a(n)_?_.

Short Answer

Expert verified

If the measures of each interior angle of a regular polygon is 108, then the polygon ispentagon.

Step by step solution

01

Step 1. Find the formula that can be used to calculate the interior angle of a regular polygon.

The interior angle of a regular polygon with n sides is 180n鈭�2n.

02

Step 2. Calculate the number of sides (n) by using the formula.

Equate the formula with the given information,

180n鈭�2n=108180n鈭�360=108n180n鈭�108n=36072n=360n=36072=5

03

Step 3. to find the type of polygon determined by n number of sides.

The number of sides n=5. Therefore, the polygon is a pentagon.

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