1950 AMC 12 第 12 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。
12.
当多边形的边数从 增加到 时，依次延长各边所形成的外角之和：
As the number of sides of a polygon increases from to the sum of the exterior angles formed by extending each side in succession:
增大
Increases
减小
Decreases
保持不变
Remains constant
无法确定
Cannot be predicted
变为 个平角
Becomes straight angles
答案：C
小提示：
想象沿多边形的边界走一周
Imagine walking once around the boundary of the polygon
大提示：
所有外角合起来表示完整转一周
The exterior angles record one complete turn
解答：
沿多边形走一周，并在每个顶点转过相应的外角，恰好完成一整圈。因此，无论边数多少，外角和始终为 。
因此，正确答案是 C。
Traversing the polygon and turning through each exterior angle makes one complete turn. Hence the sum is always independent of the number of sides.
Thus, the correct answer is C.
其他年份的第 12 题
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