Question

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?

Answer 1

(n-2)*180/n = 180 - 72, find n, then your sum is (n-2)*180

Answer 2

Sum of interior and exterior angle is 180
so
\[Interior\ angle\ = 180-72=108\]
Now we need to find the no of sides of the polygon= n
We know that interior angle of n-sides is given by
\[\frac{(n-2)\times 180}{n}\]
We have
\[(n-2)\times 180=108n\]

or
\[180n-360=108n\]
or
\[72n=360\]
n=5 sides
so
there are 5 angles each of 108 degrees
Sum of the interior angles=108+108+108+108+108=540