SOLUTION: If the complement of an angle is 15° less than one-sixth of its supplement, find the measure of the angle

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Question 156784: If the complement of an angle is 15° less than one-sixth of its supplement, find the measure of the angle
Answer by phd(3) About Me  (Show Source):
You can put this solution on YOUR website!
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 %2890-a%29%2B+15+=+%281%2F6%29%28180-a%29. Then solve for a.
Combine 90 and 15 105+-+a+=+%281%2F6%29%28180-a%29
Multiply by 6 to get rid of the fraction 630+-+6a+=+180-a
Add 6a to both sides 630+=+180+%2B5a
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.