Question 51577
Supplementary angles are those that add up to 180, and complementary angles add up to 90.  Let x represent the angle; then (180-x) is the supplementary angle and (90-x) is the complementary angle.  Three times the measure of the complement is represented by 3*(90-x) and 60 less than that produces {{{3*(90-x)-60}}}.  We're told that {{{3*(90-x)-60=180-x}}}.  So now we just solve algebraicly.  Expanding the equation produces {{{270-3x-60=180-x}}}.  Now we combine like terms to get {{{210-3x=180-x}}}.  Now add 3x to both sides to get {{{210-3x+3x=180-x+3x}}}, or {{{210=180+2x}}}.  Now subtract 180 from both sides {{{210-180=180+2x-180}}}, or {{{30=2x}}}.  Dividing both sides by 2 {{{30/2=2x/2}}} simplifies to {{{15=x}}}.  So, our angle is 15, its complement is 75, and its supplement is 165.