Problem:
The sum of all but one of the interior angles of a convex polygon equals 2570∘. The remaining angle is
Answer Choices:
A. 90∘
B. 105∘
C. 120∘
D. 130∘
E. 144∘
Solution:
The sum of the angles in a convex polygon of n sides is (n−2)180∘. Therefore, if x is the unknown angle,
(n−2)180∘=2570∘+x, with 0∘<x<180∘
If n=17, then (n−2)180∘=15(180∘)=2700∘ and x=130∘. Smaller values of n would yield negative values of x, and larger values of n would yield values of x greater than 180∘.