AMC8 2017

AMC8 2017 · Q6

AMC8 2017 · Q6. It mainly tests Triangles (properties).

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?

如果一个三角形的角度度数比例为 3 : 3 : 4，那么该三角形最大角度的度数是多少？

(A) 18 18

(B) 36 36

(D) 72 72

(E) 90 90

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let the degree measures of the angles of the triangle be $3x$, $3x$, and $4x$. Then $3x + 3x + 4x = 10x = 180$, and $x = 18$. So the largest angle has degree measure $4x = 4 \cdot 18 = 72$.

答案 (D)：设该三角形的三个角的度数分别为 $3x$、$3x$ 和 $4x$。则 $3x+3x+4x=10x=180$，所以 $x=18$。因此最大角的度数为 $4x=4\cdot 18=72$。

Topics

GE.002 Triangles (properties)