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Chapter 2: Q55. (page 95)

To find the measure of an interior angle of a regular polygon, you can use the formula m=180(n鈭�2)n, where m represents the measure of each angle and n represents the number of sides in the polygon. If m=156, how many sides does the polygon have?

Short Answer

Expert verified

The polygon has 15 sides.

Step by step solution

01

Step 1. Substitute 156 for m.

156=180(n鈭�2)n

02

Step 2. Isolate the variable.

156=180(n鈭�2)n156n=180n鈭�360360=180n鈭�156n360=24n

03

Step 3. Divide both the sides by 24.

360=24n24n24=36024n=15

Hence, the polygon has 15 sides.

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