Stephanie K. answered • 04/09/20

Experienced Math Tutor for SATs and Middle/High School Subjects

Hi Mia!

Let's set n = number of sides of the polygon, since that's what we're trying to solve.

The sum of all interior angles of a polygon is (n-2)*180° (if you want to understand how that is derived, send a follow-up and I'm happy to explain!).

This is a regular polygon, since all of the interior angles are the same. So if you divide the above, by the number of sides n, you'll get the measure of a single interior angle of the polygon: (n-2)*180° / n. Since the problem told us that measure was 150°, we can set them equal and solve for n.

(n-2)*180° / n = 150°

(n-2)*180° = 150° * n * (multiply both sides by n) *

180° * n - 360° = 150° * n * (distribute the 180°) *

180° * n = 150° * n + 360° *(add 360° to both sides) *

30° * n = 360° * (subtract 150n from both sides) *

n = 12 * (divide both sides by 30°)*

So you have your answer is 12 sides (a dodecagon!). Let me know if you have any questions, and good luck with your work!