What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 30°?

Numerical Answers Expected!

Answer for Blank 1:

Question

What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 30°?

Numerical Answers Expected!

Answer for Blank 1:

parthkohli · Answer

$$180 - \rm exterior = interior$$

parthkohli · Answer

Did you figure out the interior angle?

anonymous · Answer

150

parthkohli · Answer

Right, now for figuring out the number of sides, use the fact that the sum of exterior angles is always $360^{\circ}$.

parthkohli · Answer

Because one exterior angle is $30^{\circ}$, we can say that if there are $n$ exterior angles, then $30n = 360$.

anonymous · Answer

6 so its a hexagon which has interior angles equal to 120

parthkohli · Answer

Scroll up... you figured that the interior angle is $150$ which was correct!

anonymous · Answer

hmm...  but what about n-2.... Ohhh forgot to subtract 2 xd