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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
. Then solve for a.
Combine 90 and 15
Multiply by 6 to get rid of the fraction
Add 6a to both sides
Subtract 180 from both sides
Divide both sides by 5
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.