Question

Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 57.75 degrees. Find the measures of the angles.

Answer 1

I've seen this before

Answer 2

x + y = 90

x + y/4 = 57.75

Answer 3

Systems of equations

Answer 4

Let x and y be the two angles.


Since they are complementary, they add to 90 degrees. So x + y = 90. Solve for y to get y = 90-x


Because "The sum of the measure of the first angle and 1/4 of the second angle is 57.75", we know that x+y/4 = 57.75


Multiply every term by 4 to get 4x+y=231


4x+y=231


4x+90-x=231


4x-x=231-90


3x=141


x=141/3


x=47


y = 90-x


y = 90-47


y = 43


So the smaller angle is 43 degrees while the other angle is 47 degrees.