2017 AMC 8 Problem 6

Below is the video solution and professionally curated solution for Problem 6 of the 2017 AMC 8, 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.

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Concepts:angle sumratio and proportion

Difficulty rating: 770

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

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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