Chapter SH, Problem 11.5.3EP

To determine

The sum of measures of the interior angles of the decagon is to be estimated.

Answer to Problem 11.5.3EP

The sum of measures of the interior angles of the decagon is $1440°$ .

Explanation of Solution

Given:

Convex polygon: decagon

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 decagon that has ten sides. So,

  $n=10$

Now, use the polygon interior angles sum theorem to find out the sum of measures of the interior angles of the decagon:

  $\begin{array}{l}I=\left(n-2\right)180\\ I=\left(10-2\right)180\\ I=8\times 180\\ I=1440°\end{array}$

Conclusion:

Hence, the sum of measures of the interior angles of the decagon is $I=1440°$ .