AMC10 2011 B
AMC10 2011 B · Q7
AMC10 2011 B · Q7. It mainly tests Linear equations, Triangles (properties).
The sum of two angles of a triangle is $\frac{6}{5}$ of a right angle, and one of these two angles is 30° larger than the other. What is the degree measure of the largest angle in the triangle?
一个三角形的两个角之和是直角的 $\frac{6}{5}$，这两个角之一比另一个大 30°。该三角形最大角的度数是多少？
(A)
69
69
(B)
72
72
(C)
90
90
(D)
102
102
(E)
108
108
Answer
Correct choice: (B)
正确答案：（B）
Solution
Answer (B): The degree measures of two of the angles have a sum of $\frac{6}{5} \cdot 90 = 108 $ and a positive difference of 30, so their measures are 69 and 39. The remaining angle has a degree measure of $ 180 - 108 = 72 $, which is the largest angle.
答案 (B)：这两个角的度数之和为 $\frac{6}{5} \cdot 90 = 108 $，差为 30°，所以它们的度数为 69° 和 39°。剩余角为 $ 180 - 108 = 72° $，这是最大角。
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