2011 AMC 10B 第 7 题

Question

一个三角形中两个角的和是直角的

\frac{6}{5}

，且这两个角中的一个比另一个大

30^{\circ}

。这个三角形最大角的度数是多少？

The sum of two angles of a triangle is

\frac{6}{5}

of a right angle, and one of these two angles is

30^{\circ}

larger than the other. What is the degree measure of the largest angle in the triangle?

69

72

90

102

108

将直角的

\dfrac65

换算成度数。

Convert

\dfrac65

of a right angle to degrees

比较第三个角与那两个已知和与差的角。

Compare the third angle with the two angles whose sum and difference are known

这两个角之和为

\frac 65 \cdot 90 = 108

。所以第三个角为

180-108=72

。若这两个角中较大的为

x

，较小的为

x-30

，则

2x-30=108

，所以

x=69

。

没有角大于

72

，因此最大角是

72

。

所以正确答案是 B。

The two angles add to

\frac 65 \cdot 90 = 108.

This makes the other angle

180-108=72.

Then, if the larger of the two angles is

x

then the smaller of them is

x-30

so their sum is

2x-30=108,

making

x=69.

This means no angle is larger than

72,

making the largest equal to

72.

Thus, the correct answer is B .

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