1968 AHSME Problems/Problem 20
Problem
The measures of the interior angles of a convex polygon of sides are in arithmetic progression. If the common difference is and the largest angle is , then equals:
Solution
The formula for the sum of the angles in any polygon is . Because this particular polygon is convex and has its angles in an arithmetic sequence with its largest angle being , we can find the sum of the angles.
Plugging this into the formula for finding the sum of an arithmetic sequence...
.
Simplifying, we get .
Since we want the positive solution to the quadratic, we can easily factor and find the answer is .
Hence the answer is
See also
1968 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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.