Question 156784
Complementary angles make a right angle (90 degrees)
Supplementary angles make a straight line (180 degrees)

If the angle that we are looking for is "a" then the complement of a plus a would equal 90 degrees and 90-a would be equal to the complement. Similarly the supplement of a would be equal to 180 - a. We can write the problem as an equation {{{(90-a)+ 15 = (1/6)(180-a)}}}. Then solve for a.
Combine 90 and 15 {{{105 - a = (1/6)(180-a)}}}
Multiply by 6 to get rid of the fraction {{{630 - 6a = 180-a}}}
Add 6a to both sides {{{630 = 180 +5a}}}
Subtract 180 from both sides {{{450 = 5a}}}
Divide both sides by 5 {{{90 = a}}}

To check: The complement of 90 is 0 and the supplement of 90 is 90. Then 1/6 of the supplement is 15. 0 is 15 less than 15.