If the measure of each interior angle of a polygon is 150, how many sides does it have?

Answer 1

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!

Answer 2

If a polygon has n sides, then the total sum of its interior angles will be 180(x-2).

So we have: 150x = 180(x-2)

Dividing by 30: 5x = 6(x-2).

So 5x = 6x-12

By adding 12 to each side we get: 5x + 12 = 6x

Then we subtract 5x: 12 = x

Answer: the polygon has 12 sides, thus is a dodecagon