Chapter 2: Q55. (page 95)

To find the measure of an interior angle of a regular polygon, you can use the formula $m = \frac{180 (n - 2)}{n}$ , 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

Step 1. Substitute 156 for m.

$156 = \frac{180 (n - 2)}{n}$

Step 2. Isolate the variable.

$\begin{array}{l} 156 = \frac{180 (n - 2)}{n} \\ 156 n = 180 n - 360 \\ 360 = 180 n - 156 n \\ 360 = 24 n \end{array}$

Step 3. Divide both the sides by 24.

$\begin{array}{l} 360 = 24 n \\ \frac{24 n}{24} = \frac{360}{24} \\ n = 15 \end{array}$

Hence, the polygon has 15 sides.

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To find the measure of an interior angle of a regular polygon, you can use the formula $m = \frac{180 (n - 2)}{n}$ , 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

Step by step solution

Step 1. Substitute 156 for m.

Step 2. Isolate the variable.

Step 3. Divide both the sides by 24.

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To find the measure of an interior angle of a regular polygon, you can use the formula m=180(n−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

Step by step solution

Step 1. Substitute 156 for m.

Step 2. Isolate the variable.

Step 3. Divide both the sides by 24.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Applied Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

To find the measure of an interior angle of a regular polygon, you can use the formula $m = \frac{180 (n - 2)}{n}$ , 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?