1960 AHSME Problems/Problem 27
Problem
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
Solution
Let be the interior angle of the nth vertex, and let be the exterior angle of the nth vertex. From the conditions in the problem, That means Since the sum of the exterior angles of a polygon is , the equation can be simplified as The sum of the interior angles is degrees. However, there is no other constraint on what angle the interior angles can be, so we can not for sure claim that the polygon is regular or not. Thus, the answer is .
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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