2017 AMC 12A Problems/Problem 11
Problem
Claire adds the degree measures of the interior angles of a convex polygon and arrives at a sum of . She then discovers that she forgot to include one angle. What is the degree measure of the forgotten angle?
Solution
We know that the sum of the interior angles of the polygon is a multiple of . Note that and , so the angle Claire forgot is . Since the polygon is convex, the angle is , so the answer is .
Solution 2 (fast with answer choices)
Because the sum of the interior angles is a multiple of 180, we know that the sum of the angles in a polygon is 0 mod 9. 2017 is congruent to 1 mod 9, so the answer has to be -1 mod 9. The only answer that is -1 mod 9 is 143. -harsha12345
See Also
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.