SOLUTION: Angles A and B are complementary. Find the measures of each angle. Angle A = 3/4x - 13 Angle B = 3x - 17

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Question 883051: Angles A and B are complementary. Find the measures of each angle.
Angle A = 3/4x - 13
Angle B = 3x - 17
Answer by Leaf W.(135) About Me  (Show Source):
You can put this solution on YOUR website!
Hello!
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Complementary angles, by definition, are angles whose measures add up to 90 degrees. Therefore,
Angle A + Angle B = 90
Using the given expressions,
%28%283%2F4%29x+-+13%29+%2B+%283x+-+17%29+=+90
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Now solve for x!
%283%2F4%29x+-+13+%2B+3x+-+17+=+90
Group together like terms: %283%2F4%29x+%2B+3x+-+13+-17+=+90
Find a common denominator: %283%2F4%29x+%2B+%2812%2F4%29x+-+13+-+17+=+90
Add like terms: %2815%2F4%29x+-+30+=+90
Add 30 to both sides: %2815%2F4%29x+=+120
Multiply both sides by 4%2F15: x = 32
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Now plug x into your expressions to find A and B:
Angle A = %283%2F4%29x+-+13+=+%283%2F4%29%2832%29+-+13+=+24+-+13+=+11
Angle B = 3x - 17 = 3(32) - 17 = 96 - 17 = 79
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Thus, Angle A is 11 degrees and Angle B is 79 degrees.
I hope this helps! =)