Problem 27 · 2017 Math Kangaroo
Stretch
Geometry & Measurement
Number Theory
arithmetic-sequencedivisibility
Lisa places some points on a circle and then connects them in sequence to make a polygon. She adds up the interior angles of the polygon. By mistake she misses out one angle and obtains the sum 2017. How big is the angle that she has overlooked?
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Answer: E — 143°
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Hint 1 of 2
The true angle sum of a polygon is a multiple of 180°.
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Hint 2 of 2
The missed angle is the gap up to the next multiple of 180 above 2017.
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Approach: round up to the nearest valid polygon angle sum
- The interior angles of an n-gon sum to (n−2)·180°, a multiple of 180.
- The smallest multiple of 180 above 2017 is 2160 = 12·180.
- The overlooked angle is 2160 − 2017 = 143°, choice E.
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