Chapter SH, Problem 11.5.8EP

To determine

The sum of measures of the interior angles of the $15$ -gon is to be estimated.

Answer to Problem 11.5.8EP

The sum of measures of the interior angles of the $15$ -gon is $2340°$ .

Explanation of Solution

Given:

Convex polygon: $15$ -gon

Concept Used:

The polygon interior angles sum theorem is given by the following expression:

  $I=\left(n-2\right)180$

Where,

Sides of polygon: $n$

Calculation:

The name of the given polygon is $15$ -gon that has $15$ sides. So,

  $n=15$

Now, use the polygon interior angles sum theorem to find out the sum of measures of the interior angles of the $15$ -gon:

  $\begin{array}{l}I=\left(n-2\right)180\\ I=\left(15-2\right)180\\ I=13\times 180\\ I=2340°\end{array}$

Conclusion:

Hence, the sum of measures of the interior angles of the $15$ -gon is $I=2340°$ .