SOLUTION: My second question is: What is the measure of the smaller angle of two supplementary angles if twice the larger angle is ten less than three times the smaller angle? Thank You so m

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Question 326007: My second question is: What is the measure of the smaller angle of two supplementary angles if twice the larger angle is ten less than three times the smaller angle? Thank You so much!
Answer by jessica43(140) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this problem, you are going to have to write two equations using what you know.
First, you know that you have two supplementary angles. This means that together the angles add up to 180 degrees. So:
A + B = 180 (where A = measure of the larger angle, B = measure of the smaller angle)
Second, you now that twice the larger angle (A) is ten less than three times the smaller angle (B):
2A = 3B - 10
This can be rewritten as:
A = (3/2)B - 5 (I divided each side by 2)
Now you can plug in the second equation into the first and solve for B:
A + B = 180
((3/2)B - 5) + B = 180
(5/2)B - 5 = 180
(5/2)B = 185
B = 74
Finally, plug this value into the first equation to find A:
A + B = 180
A + 74 = 180
A = 106
So angle A is 106 degrees and angle B is 74 degrees.