SOLUTION: the measure of angle A is 38 less than its complement. find the measure of angle A

Question 322620: the measure of angle A is 38 less than its complement. find the measure of angle A

Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
The definition of complementary angles is two acute angles that add up to 90 degrees. Written as a formula:
A+B = 90 (A= measure of angle A, B=measure of angle B, A and B are complementary)
We also know that angle A is 38 degrees less than B. So you can also write this as a formula:
A = B-38
Now we can combine these formulas by plugging formula two into formula one for A and solving for B:
A+B = 90
(B-38) + B = 90
2B - 38 = 90
2B = 128
B = 64
So the measure of angle B is 64 degrees. Now plug this into formula two to find A:
A = B-38
A = 64-38
A = 26
The measure of angle A is 26 degrees.
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