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

Algebra ->  Coordinate Systems and Linear Equations -> 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       Log On


   

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) About Me  (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 x%2By=90


"The sum of the measure of the first angle and one-fourth the second angle is 63.75 degrees" translates to this equation:
x%2B%281%2F4%29y=63.75


4%28x%2B%281%2F4%29y%29=4%2863.75%29 Multiply both sides by the LCD 4 to clear the fraction


4x%2By=255 Multiply


So we have the system of equations:


system%28x%2By=90%2C4x%2By=255%29


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

x%2By=90 Start with the first equation


y=90-x Subtract x from both sides


y=-x%2B90 Rearrange the equation




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

Since y=-x%2B90, we can now replace each y in the second equation with -x%2B90 to solve for x



4x%2Bhighlight%28%28-x%2B90%29%29=255 Plug in y=-x%2B90 into the first equation. In other words, replace each y with -x%2B90. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x%2B90=255 Combine like terms on the left side


3x=255-90Subtract 90 from both sides


3x=165 Combine like terms on the right side


x=%28165%29%2F%283%29 Divide both sides by 3 to isolate x



x=55 Divide





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


So the first part of our answer is: x=55









Since we know that x=55 we can plug it into the equation y=-x%2B90 (remember we previously solved for y in the first equation).



y=-x%2B90 Start with the equation where y was previously isolated.


y=-%2855%29%2B90 Plug in x=55


y=-55%2B90 Multiply


y=35 Combine like terms



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


So the second part of our answer is: y=35









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

So our answers are:

x=55 and y=35


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