Question

If the sum of interior angle measures of a polygon is ${900}^{\circ }$ , how many sides does the polygon have?

Answer 1

Hint: In order to determine the sides of the polygon whose sum of interior angles measure ${900}^{\circ }$ , we will use the formula $Interioranglesofaregularpolygon={180}^{\circ }\left(n\right)-{360}^{\circ }$ , as the sum of the interior angle of a polygon is given. We will determine the $n$ by substituting the value of the sum of interior angles of a polygon and evaluate it.

Complete step-by-step answer:
We know that from interior angles of a polygon, the sum of interior angles of a polygon is given by the formula,
 $Interioranglesofaregularpolygon={180}^{\circ }\left(n-2\right)$
Where $n$ is the number of sides.
It is given that the sum of interior measures of a polygon is ${900}^{\circ }$ .
Therefore, ${900}^{\circ }={180}^{\circ }\left(n\right)-{360}^{\circ }$
 $180n=900+360$
 $180n=1260$
  $n={\displaystyle \frac{1260}{180}}$
 $n=7$
Hence, the sides of the polygon whose sum of interior angles measure ${900}^{\circ }$ is $7$
So, the correct answer is “7”.

Note: An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. In other words, the angles measure at the interior part of a polygon is called the interior angle of a polygon.