SOLUTION: how do you find two supplement angles in the ratio of7:5?

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Question 120571: how do you find two supplement angles in the ratio of7:5?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I think you meant to say 'supplemental' angles.

Supplemental angles are angles whose measures sum to either 180 degrees or pi, depending on the measurement system you are using. Let's use 180 degrees for this example.

If the measure of one of the angles is x degrees, then the measure of the other angle must be 180 - x degrees. And we know that these two angles are in the ratio of 7:5. So we can write:

%28180-x%29%2Fx=7%2F5

Since we have created a proportion, we can cross multiply and solve:

5%28180-x%29=7x

900-5x=7x

900=12x

x=75.

So 75 degrees is the measure of one of the angles, and the other angle must then be 180 - 75 = 105.

Check the answer:
Reduce the fraction 105%2F75 to lowest terms.

105%2F75=%2815%2A7%29%2F%2815%2A5%29=7%2F5, answer checks.