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An Arithmetic Sequence of Sectors

Source: 2012 AMC 12A Problem #7 and AMC 10A Problem #10

February 8, 2012
AMC

Problem Statement

Mary divides a circle into 1212 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?
<spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 10<spanclass=′latex−bold′>(E)</span> 12 <span class='latex-bold'>(A)</span>\ 5\qquad<span class='latex-bold'>(B)</span>\ 6\qquad<span class='latex-bold'>(C)</span>\ 8\qquad<span class='latex-bold'>(D)</span>\ 10\qquad<span class='latex-bold'>(E)</span>\ 12
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