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 $ Interior{\text{ }}angles{\text{ }}of{\text{ }}a{\text{ }}regular{\text{ }}polygon = 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,
 $ Interior{\text{ }}angles{\text{ }}of{\text{ }}a{\text{ }}regular{\text{ }}polygon = 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 = \dfrac{{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.