AMC 8 2014 Problem 15

AMC8 2014 年第 15 题

圆★★★☆☆

The circumference of the circle with center O is divided into 12 equal arcs, marked the letters A through L as seen below. What is the number of degrees in the sum of the angles x and y ?

如下图所示，圆心为 O 的圆被分成 12 个相等的圆弧，由字母 A 到 L 标识。那么角 x 和角 y 的度数之和是多少？

A.75
B.80
C.90
D.120
E.150

正确答案 · Correct Answer

解析 · Solution

Solution 1

The measure of an inscribed angle is half the measure of its corresponding central angle. Since each unit arc is

\displaystyle \frac{1}{12}

of the circle's circumference, each unit central angle measures

\displaystyle \frac{360}{12}^{\circ} = 30^{\circ}

. From this,

\angle EOG = 60^{\circ}

, so

x = 30^{\circ}

. Also,

\angle AOI = 120^{\circ}

, so

y = 60^{\circ}

. The number of degrees in the sum of both angles is 30 + 60 = 90.

继续练习

免费刷 2014 整卷 →