Question

What is the sum of the angles in a $7$ sided polygon?

Answer 1

Hint: According to the given question, we have been asked to calculate the sum of all the angles in a seven sided polygon. For that we have to use the formula for calculating the sum of the interior angles of a polygon having a total of n number of sides. The formula is given by the expression \[S=\left( n-2 \right)\times {{180}^{\circ }}\], where n is the number of sides of the polygon. In the above question, it has been mentioned that the polygon is seven sided, which means that the number of sides in the polygon will be equal to seven so that we can substitute $n=7$ in the formula \[S=\left( n-2 \right)\times {{180}^{\circ }}\] to get the required sum of the angles.

Complete step by step answer:
We know that the sum of the interior angles of a polygon having n number of sides is given by the formula
$\Rightarrow S=\left( n-2 \right)\times {{180}^{\circ }}$
According to the above question, the given polygon is a seven sided polygon. This means that the total number of sides is equal to seven. So the polygon will look like

Therefore, we can substitute $n=7$ in the above formula to get the required sum of the interior angles of the given polygon as
$\begin{align}
  & \Rightarrow S=\left( 7-2 \right)\times {{180}^{\circ }} \\
 & \Rightarrow S=5\times {{180}^{\circ }} \\
\end{align}$
On solving we finally get
$\Rightarrow S={{900}^{\circ }}$
Hence, we have got the required sum of the seven sided polygon as ${{900}^{\circ }}$.

Note: We must note that the formula used in the above solution is not only valid for a regular polygon, but for any kind of polygon of given number of sides. Although in the figure we have considered a regular polygon of seven sides, the sum of the interior angles would be equal to ${{900}^{\circ }}$ for any polygon having seven sides.