Question 151328
Two angles are complementary. The sum of the measure of the first angle and one-fourth the second angle is 60.75. What is the measure of the smaller angle & what is the measure of the other?
:
Let the two angles = x & y
:
"Two angles are complementary."
x + y = 90
x = 90 - y
:
" The sum of the measure of the first angle and one-fourth the second angle is 60.75."
x + .25y = 60.75 
:
Substitute (90-y) for x in the above equation
(90-y) + .25y = 60.75
:
-1.0y + .25y = 60.75 - 90
:
-.75y = -29.25
y = {{{(-29.25)/(-.75)}}}
y = 39 degrees is the smaller angle
then
x = 90 - 39 = 51 degrees
:
:
Check solution in the statement:
"The sum of the measure of the first angle and one-fourth the second angle is 60.75.
51 + .25(39) =
51 + 9.75 = 60.75