2012 AMC 12A 第 7 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
7.
Mary 将一个圆分成 个扇形。这些扇形的圆心角用度数表示时都是整数，并且构成一个等差数列。最小的扇形角可能是多少度？
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?
小提示：
十二个角的和为
The twelve angles sum to
大提示：
若首项为 ，公差为 ，则 ，所以
With first term and common difference so
解答：
设最小角为 ，公差为 。所有角的和为 ，所以 。
要使 小，就让 尽量大。由于 必须为偶数， 为偶数，而 给出 ，所以 。更大的偶数 会使 非正。
因此，正确答案是 C。
Let be the smallest angle and the common difference. The sum of the angles is so
To make small, take large. Since must be even, is even, and gives so A larger even makes non-positive.
Thus, the correct answer is C.
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