Question 578709
We have


*[tex \LARGE 180(n-1) = 2270 + k] where k is the unknown angle.


Since k is between 0 and 180 (convex polygon), 180(n-1) must be a little more than 2270. Since 180*12 = 2160 and 180*13 = 2340, we conclude that n-1 = 13, so n = 14.