1976 AHSME Problems/Problem 14
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.