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 1
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 , we know that the sum of the angles in a polygon is . is congruent to , so the answer has to be . The only answer that is congruent to is . -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 |
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