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 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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