Problem:
Mary divides a circle into sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
Answer Choices:
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Solution:
Let be the initial term and the common difference for the arithmetic sequence. Then the sum of the degree measures of the central angles is
so . Letting yields the smallest possible positive integer value for , namely .
The problems on this page are the property of the MAA's American Mathematics Competitions