1973 AHSME Problems/Problem 16
Problem
If the sum of all the angles except one of a convex polygon is , then the number of sides of the polygon must be
Solution
Let be the number of sides in the polygon. The number of interior angles in the polygon is . We know that the sum of all but one of them is , so the sum of all the angles is more than that.
The sum of the angles in a 15-sided polygon is , making the remaining angle . The angles of a convex polygon are all less than , and since adding one more side means adding to the measure of the remaining angle, we can confirm that there are sides in the polygon.
See Also
1973 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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