Question

Complete each sentence with the most appropriate word, phase or value.

If the measure of each interior angle of a polygon is 144, then the polygon has ________ sides.

Short answer

The answer is 10.

Step-by-step solution

- State the formula to used. 

The sum of interior angles of a polygon is equal to ${180}^{\circ }(n-2)$

- State the explanation.

Let n be the number of sides of the polygon.

Then, the sum of interior angles of polygon is$144n$ .

Then,

$\begin{array}{c}144n={180}^{\circ }(n-2)\\ 144n-180n=-360\\ 36n=360\\ n=10\end{array}$

Hence, the polygon has 10 sides.

- State the conclusion.

Therefore,

“If the measure of each interior angle of a polygon is 144, then the polygon has 10sides.”