AMC 12A 2012 #7

[nsguy1350]

Mary divides a circle into 12 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?

[darksaber21]

If the integers are all in a sequence, and all add up to 360, then we can formulate:
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Since we need a to be an integer, we start plugging in values in multiples of two. That's what I did anyway. Eventually, you'll hit negative numbers, so plug numbers for multiples of two for d until that occurs, so you can find the smallest number, which happens to be:
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Plug in a six for d, and you will get -3, so plug in a four to get your answer.