Question

Find the sum of the exterior angles in a pentagon.

Answer 1

We know that the formula to calculate the sum of interior angles of a polygon with $n$ sides is $(n-2)\times 180°$

Hence, each interior angle $=\left[\frac{(n-2)\times 180°}{n}\right]$

We know that each exterior angle is supplementary to the interior angle.

Now, from the above formula, we can derive each exterior angle $=\left[\frac{180°n-180°n+360°}{n}\right]=\frac{360°}{n}$

So, the sum of exterior angles of a polygon $=n\left(\frac{360°}{n}\right)$

As the number of sides in a pentagon is $5,n=5$

The sum of exterior angles of a pentagon $=5\left(\frac{360°}{5}\right)=360°$.

Hence, the sum of the exterior angles of a pentagon is $360°$.