SOLUTION: One angle is twice its supplement increased by 21 degrees. Find the measures of the two supplementary angles.

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Question 502589: One angle is twice its supplement increased by 21 degrees. Find the measures of the two supplementary angles.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let x and y be your two angles. Let y be the larger angle.

Because x and y are supplementary angles, we know that x%2By=180

Since "One angle is twice its supplement increased by 21 degrees", this means that y=2x%2B21

x%2By=180

x%2B%282x%2B21%29=180

x%2B2x%2B21=180

3x%2B21=180

3x=180-21

3x=159

x=159%2F3

x=53

So the smaller angle is 53 degrees.

The larger angle is then y=2x%2B21=2%2853%29%2B21=106%2B21=127 degrees.

So the two angles are 53 degrees and 127 degrees