Chapter 11.3, Problem 6GP

a.

To determine

To determine the measure of one interior angle of the nonagon.

Answer to Problem 6GP

  $140°$

Explanation of Solution

Given:

Nonagon

  

Formula used:

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

Calculation:

  

The nonagon has $9$ sides, $n=9.$

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$ , where $n$ represents number of sides.

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(9-2\right)\times 180}{9}$

  $\Rightarrow$ The measure of one interior angle $=\frac{7\times 180}{9}$

  $\Rightarrow$ The measure of one interior angle $=\frac{1260}{9}$

  $\Rightarrow$ The measure of one interior angle $=140°$

Conclusion:

Therefore, the measure of one interior angle of the nonagon is $140°.$

b.

To determine

To determine the measure of one interior angle of the heptagon.

Answer to Problem 6GP

  $128.57°$

Explanation of Solution

Given:

Heptagon

  

Formula used:

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

Calculation:

  

The nonagon has $7$ sides, $n=7.$

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$ , where $n$ represents number of sides.

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(7-2\right)\times 180}{7}$

  $\Rightarrow$ The measure of one interior angle $=\frac{5\times 180}{9}$

  $\Rightarrow$ The measure of one interior angle $=\frac{900}{7}$

  $\Rightarrow$ The measure of one interior angle $=128.57°$

Conclusion:

Therefore, the measure of one interior angle of the heptagon is $128.57°.$

c.

To determine

To determine the measure of one interior angle of the 20-gon.

Answer to Problem 6GP

  $162°$

Explanation of Solution

Given:

20-gon

Formula used:

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

Calculation:

The nonagon has $20$ sides, $n=20.$

The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$ , where $n$ represents number of sides.

  $\Rightarrow$ The measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}$

  $\Rightarrow$ The measure of one interior angle $\text{=}\frac{\left(20-2\right)\times 180}{7}$

  $\Rightarrow$ The measure of one interior angle $=\frac{18\times 180}{20}$

  $\Rightarrow$ The measure of one interior angle $=\frac{3240}{20}$

  $\Rightarrow$ The measure of one interior angle $=162°$

Conclusion:

Therefore, the measure of one interior angle of the 20-gon is $162°.$