SOLUTION: Two angles are complementary. The measure of one angle is 2° more than three times the measure of the other. Find the measure of each angle.

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Question 430767: Two angles are complementary. The measure of one angle is 2° more than three times the measure of the other. Find the measure of each angle.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Let A and B be the angles.
They're complementary, so we know: A+B = 90
The problem also states that one angle is 2 degrees more than 3 times the other angle.
A = 3B + 2
.
Since A+B=90
B = 90-A
A = 90-B
.
Substituting
90-B = 3B+2
Add B to both sides
90 = 4B +2
Subtract 2 from both sides
88 = 4B
so
4B = 88
Divide both sides by 4
B = 22
.
Substitute back into a prior equation to find A
A = 90 - B
A = 90 - 22
A = 68
.
Always check your work.
Use the first equation to see if it is true
A = 3B + 2 ?
68 = 3(22) + 2 ?
68 = 66 + 2
True
.
Now re-read the question to make sure you answer it.
Answer: The measures of the two angles are 68 degrees and 22 degrees.
.
Done.