2014 AMC 8 第 15 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。
15.
圆心为 的圆周被分成 段相等的弧，并如图标上字母 到 。角 与 的和是多少度？
The circumference of the circle with center is divided into equal arcs, marked the letters through as seen below. What is the number of degrees in the sum of the angles and
小提示：
相邻两个字母在圆心处截出的角为
Each adjacent pair of letters cuts off at the center.
大提示：
两个相关三角形都是等腰三角形，因为它们的边是半径
The two relevant triangles are isosceles because their sides are radii.
解答：
段弧等分圆周，所以每段弧对应的圆心角为 。
跨过 段弧，所以 类似地，我们还知道这两个三角形都是等腰三角形，因为它们各有两条边是半径。因此 且 所以 。
所以正确答案是 C。
Note that each of the arcs splits the circle evenly, so they each cover
spans of these arcs, so Similarly, We also know that both triangles are isosceles since two of their sides are radii. Therefore, and Therefore,
Thus, C is the correct answer.
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