1960 AMC 12 Problem 27
Attempt Problem 27 of the 1960 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1960 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
27.
Let be the sum of the interior angles of a polygon for which each interior angle is times the exterior angle at the same vertex. Then:
and may be regular
and is not regular
and is regular
and is not regular
and may or may not be
regular
Answer: E
Small hint:
An interior angle and its corresponding exterior angle sum to
Big hint:
The condition fixes every angle but says nothing about the side lengths
Solution:
If an exterior angle is then so Since the exterior angles total the polygon has vertices and All its angles are equal, but its sides need not be equal, so it may or may not be regular.
Thus, the correct answer is E.
Problem 27 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
- 1964 AMC 12
- 1965 AMC 12
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- 1972 AMC 12
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- 1978 AMC 12
- 1979 AMC 12
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- 1999 AMC 12