SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-forth the second angle is 81.75 degrees. Find the measure of the angles. What is the measure of

Algebra ->  Angles -> SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-forth the second angle is 81.75 degrees. Find the measure of the angles. What is the measure of      Log On


   

Question 162283: Two angles are complementary. The sum of the measure of the first angle and one-forth the second angle is 81.75 degrees. Find the measure of the angles.
What is the measure of the smaller angle? ____ degrees
What is the measure of the other angle? ______ degrees
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Let A1 be the first angle and A2 be the second angle. Since they are complementary, you can write the following equation:
Equation #1: A1%2BA2=90
From the given information, you can also write this equation:
Equation #2: A1%2B%280.25%29A2=81.75
Now you have 2 equations and 2 unknowns, so you can solve the problem.
First, solve equation #1 for A1:
A1=90-A2
Next, substitute this expression for A1 into Equation #2:
90-A2%2B0.25%2AA2=81.75
Now, you can solve for A2:
-A2%2B0.25%2AA2=81.75-90
-0.75%2AA2=-8.25
highlight%28A2=11%29
Next, just plug this value for A2 into equation #1 and you will have the value for A1. I will leave this part to you :-)
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Good Luck,
tutor_paul@yahoo.com