SOLUTION: I need help with this problem: Two angles are complimentary. The sum of the measure of the first anagle and one-fourth the second angle is 66degrees. What is the measure of the sma

Algebra ->  Angles -> SOLUTION: I need help with this problem: Two angles are complimentary. The sum of the measure of the first anagle and one-fourth the second angle is 66degrees. What is the measure of the sma      Log On


   

Question 336127: I need help with this problem: Two angles are complimentary. The sum of the measure of the first anagle and one-fourth the second angle is 66degrees. What is the measure of the smaller angle?
What is the measure of the other angle whose sum is 90degrees?
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Two angles are complimentary
this means: A+B=90
---
The sum of the measure of the first anagle and one-fourth the second angle is 66degrees
This means: A+(1/4)*B=66
---
you have two equations in two unknowns.
Solve the A+B=90 for one of the angles (does not matter which, say A)
A=90-B
--
Substitute A=90-B into second equation
A+(1/4)*B=66; (90-B)+(1/4)*B=66
--
solve for B
90-(3/4)*B=66
-(3/4)*B=66-90=-24
B=(-24)*(-4/3)=32
--
substitute B=32 into A=90-B=90-32=58