AMC 8 2017 Problem 6
AMC8 2017 年第 6 题
三角形★☆☆☆☆
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?
如果一个三角形的三个角度数之比为 3：3：4，那么这个三角形的最大的角是多少度？
- A.18
- B.36
- C.60
- D.72
- E.90
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
The sum of the ratios is 10. Since the sum of the angles of a triangle is , the ratio can be scaled up to 54:54:72 (). The numbers in the ratio 54:54:72 represent the angles of the triangle. The question asks for the largest, so the answer is 72.
We can denote the angles of the triangle as , , . Due to the sum of the angles in a triangle, . The greatest angle is and after substitution we get 72.
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