Question

如果一个三角形的角度之比为 $3:3:4$ ，那么这个三角形最大角的度数是多少？

If the degree measures of the angles of a triangle are in the ratio $3:3:4,$ what is the degree measure of the largest angle of the triangle?

$18$

$36$

$60$

$72$

$90$

答案：D

知识点：角度和比与比例

难度评级：770

小提示：

设三个角分别为 $3x$ 、 $3x$ 和 $4x$

Let the three angle measures be $3x,$ $3x,$ and $4x$ .

大提示：

三角形内角和为 $180^\circ$

The angles of a triangle add to $180^\circ$ .

视频讲解：

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文字解答：

设三个角为 $3x$ 、 $3x$ 和 $4x$ 。它们的和为 $180$ ，所以 $3x + 3x + 4x = 180$ ，即 $10x = 180$ ，从而 $x = 18$ 。

最大角为 $4x = 72$ 。

所以正确答案是 D。

We can let the three angles be equal to $3x,$ $3x,$ and $4x.$ Then we know that their sum equals $180.$ From this we can set $3x + 3x + 4x = 180,$ and solving this, we get $10x = 180$ and $x = 18.$

The largest angle is $4x = 72.$

Thus, D is the correct answer.

2017 AMC 8 第 6 题