Chapter 11.3, Problem 18IP

To determine

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

Answer to Problem 18IP

  $135°$

Explanation of Solution

Given:

Octagon

  

Formula used:

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

Calculation:

  

The Octagon has $8$ sides, $n=8.$

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 $=\frac{\left(8-2\right)\times 180}{8}$

  $\Rightarrow$ The measure of one interior angle $=\frac{6\times 180}{8}$

  $\Rightarrow$ The measure of one interior angle $=\frac{1080}{8}$

  $\Rightarrow$ The measure of one interior angle $=135°$

Conclusion:

Therefore, the measure of one interior angle of the Octagon is $135°.$