Question

What is the sum of interior angles in a hexagon?

Answer 1

Hint: To obtain the sum of the interior angle we will use the general formula to find the sum of interior angles of polygon. Firstly we will find the number of sides of a hexagon then we will write the general formula to find the sum of interior angles of the polygon and substitute the value in it, Finally solve the obtained equation to get the desired answer.

Complete step-by-step answer:
The polygon given in the question is hexagon.
We know there are 6 sides of a Hexagon - polygon so:
$n=6$
The general formula to find the sum of interior angle of polygon is given as below:
$180\left( n-2 \right)$
Put $n=6$ in above formula for finding the sum of interior angle of a Hexagon and simplify it as follows:
$\begin{align}
  & 180\left( 6-2 \right) \\
 & \Rightarrow 180\times 4 \\
 & \therefore 720 \\
\end{align}$
So the value obtained is 720.
Hence the sum of the interior angle of a Hexagon is 720.

Note: A polygon is a plane figure that is made by a finite number of straight line segments which all are connected by a closed polygon chain. A polygon has edges and sides and two edges meet to form a vertex. The sum of interior angle of a polygon is $180\left( n-2 \right)$ because a $n$-gon polygon is considered to be made up of two $n-2$ triangles and sum of interior angle of a triangle is ${{180}^{\circ }}$. One of the properties of Hexagon is it can tile the plane. Each exterior angle of a Hexagon is ${{60}^{\circ }}$ and there are 9 diagonals in a Hexagon.