1976 AHSME Problems/Problem 14
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Problem 14
The measures of the interior angles of a convex polygon are in arithmetic progression. If the smallest angle is , and the largest is , then the number of sides the polygon has is
Solution
Let equal the number of sides the polygon has. The sum of all the interior angles of a polygon is: .
The formula for an arithmetic series is . Set this equal to and solve. In this case, and .
Our equation becomes .
Simplifying, we get ~jiang147369
See Also
1976 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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