Chapter 11.3, Problem 44STP

To determine

To find the measure in degrees of an interior angle of a regular polygon with 20 sides.

Answer to Problem 44STP

  ${162}^0$

Explanation of Solution

Given:

A regular polygon with 20 sides.

Formula used:

Sum of the interior angles of a regular polygon: ${180}^0\times \left(n-2\right)$ where $n$ is the number of sides of the given polygon.

Calculation:

Now according to the formula of sum of interior angles of a regular polygon,

  $\Rightarrow {180}^0\times \left(n-2\right)$ ….(i).

Now putting $n=20$ in equation (i),

  $\Rightarrow {180}^0\times \left(20-2\right)$

  $\Rightarrow {180}^0\times 18$

  $\Rightarrow {3240}^0$

Sum of the measures of the interior angle of the polygon with 20 sides: ${3240}^0$

Now to find the measure of one angle, divide ${3240}^0$ by $20$ ,

  $\Rightarrow \frac{{3240}^0}{20}$

  $\Rightarrow {162}^0$

Conclusion:

Therefore, the measure of an interior angle of a regular polygon with 20 sides is ${162}^0$ .