SOLUTION: Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 63.75 degrees. Find the measure of the angles. What is the measure of

Question 146410: Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 63.75 degrees. Find the measure of the angles.
What is the measure of the smaller angle?
What is the measure of the other angle?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
let x=measure of angle 1 and y=measure of angle 2

"Two angles are complementary" tells us that the first equation is

"The sum of the measure of the first angle and one-fourth the second angle is 63.75 degrees" translates to this equation:

Multiply both sides by the LCD 4 to clear the fraction

Multiply

So we have the system of equations:

Now let's use substitution to solve this system

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Combine like terms on the left side

Subtract 90 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and

So the measure of smaller angle is 35 degrees and the measure of the other angle is 55 degrees
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