Question

one exterior angle of a regular polygon measures 72 degrees. what is the measure of one interior angle?

Answer 1

We are given that an exterior angle of a polygon measures 72 degrees. To determine the interior angle we need to have into account that the sum of the interior and exterior angles of a regular polygon adds up to 180 degrees. Therefore:

`72+x=180`

Where "x" is the interior angle. Now, we solve for "x" by subtracting 72 from both sides:

`\begin{gathered} 72-72+x=180-72 \\ x=108 \end{gathered}`

Therefore, the measure of the interior angle is 108