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

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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