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:
[tex]72+x=180[/tex]Where "x" is the interior angle. Now, we solve for "x" by subtracting 72 from both sides:
[tex]\begin{gathered} 72-72+x=180-72 \\ x=108 \end{gathered}[/tex]Therefore, the measure of the interior angle is 108
