SOLUTION: I am planning on taking the Accuplacer test in a few days and am stuck on this question. "One angle of a triangle measures 30 degrees. Of the remaining two angles, the larger one i

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Question 1117771: I am planning on taking the Accuplacer test in a few days and am stuck on this question. "One angle of a triangle measures 30 degrees. Of the remaining two angles, the larger one is twice as large as the smaller one. What is the measure of the smaller angle?" I got it wrong and their response was that the interior of a triangle is 180 degrees and the larger one was 50 degrees. They gave this work up.
180-30=150
2X+x=3X
3X=150
3X/3=150/3
The answer came out to 50. But I do not understand how. If one angle is 30 degrees how can the larger one be twice as large as the smaller one and come to 50 degrees? It does not add up. They subtracted 30 from 180 and got 150. Wouldn't that just leave 2 sides left?
Thank you
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
All angles in a triangle total so The smaller angle is x.

I hope you understand now.
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

I am planning on taking the Accuplacer test in a few days and am stuck on this question. "One angle of a triangle measures 30 degrees. Of the remaining two angles, the larger one is twice as large as the smaller one. What is the measure of the smaller angle?" I got it wrong and their response was that the interior of a triangle is 180 degrees and the larger one was 50 degrees. They gave this work up.
180-30=150
2X+x=3X
3X=150
3X/3=150/3
The answer came out to 50. But I do not understand how. If one angle is 30 degrees how can the larger one be twice as large as the smaller one and come to 50 degrees? It does not add up. They subtracted 30 from 180 and got 150. Wouldn't that just leave 2 sides left?
Thank you
They did say that one angle is 30o, and that "Of the remaining two angles, the larger one is twice as large as the smaller one."

Since one angle is 30o, then the other 2 SUM to 150o(180 - 30)

Therefore, let the smaller of the 2 REMAINING ANGLES be S

Then the larger of the 2 REMAINING angles is 2S

We then get: S + 2S = 150

3S = 150

The smaller of the 2 REMAINING angles, or  

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