Question 87937
Two angles are complementary. One-half the measure of the larger angle exceeds one-fourth the measure of the smaller by 30. Find the measure of the angle, the measure of its supplement and the measure of its complement.

let the smaller angle be x
then the larger angle =  (90-x)
now according to the sum we have
1/2(90-x) = x/4 + 30

==>  45-x/2 = x/4 + 30

==>  45 -x/2+x/2 = x/4+x/2 + 30

==>  45 -30 = x/4+x/2 +30 - 30

==>  15  = x+2x/4

==>  15*4 = x+2x/4*4

==>  60 = 3x

==>  60/3 = 3x/3
 
==>  20 = x

 hence the smaller angle is 20 degree and the larger angle = 90-x  i.e 90-20  = 70 degree