Chapter 11.3, Problem 14IP

To determine

To determine the sum of the measure of the interior angles of each polygon.

Answer to Problem 14IP

  $1440°$

Explanation of Solution

Given:

Decagon

  

Formula used:

The sum of the measure of the interior angles $= \left(n-2\right)\times 180$

Calculation:

  

The decagon has $10$ sides, $n=10.$

The sum of the measure of the interior angles $= \left(n-2\right)\times 180$ , where $n$ represents number of sides.

  $\Rightarrow$ The sum of the measure of the interior angles $= \left(n-2\right)\times 180$

  $\Rightarrow$ The sum of the measure of the interior angles $= \left(10-2\right)\times 180$

  $\Rightarrow$ The sum of the measure of the interior angles $=8\times 180$

  $\Rightarrow$ The sum of the measure of the interior angles $=1440°$

Conclusion:

Therefore, the sum of the measure of the interior angles is $1440°.$