2017 AMC 8 Problem 6

Attempt Problem 6 of the 2017 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2017 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

6.

If the degree measures of the angles of a triangle are in the ratio 3:3:4,3:3:4, what is the degree measure of the largest angle of the triangle?
18 18
36 36
60 60
72 72
90 90
Answer: D
Concepts:angle sumratio and proportion
Small hint:
Let the three angle measures be 3x,3x, 3x,3x, and 4x4x.
Big hint:
The angles of a triangle add to 180∘180^\circ.
Video solution:
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Written solution:
We can let the three angles be equal to 3x,3x, 3x,3x, and 4x.4x. Then we know that their sum equals 180.180. From this we can set 3x+3x+4x=180,3x + 3x + 4x = 180, and solving this, we get 10x=18010x = 180 and x=18.x = 18.
The largest angle is 4x=72.4x = 72.
Thus, D is the correct answer.
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