SOLUTION: If half of the complement of a certain angle is 1° more than one-sixth of the supplement of the angle, find the angle.

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Question 1058013: If half of the complement of a certain angle is 1° more than one-sixth of the supplement of the angle, find the angle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Give "the angle" a variable, x.
system%28x%2By=90%2Cx%2Bw=180%2Cy%2F2=1%2Bw%2F6%29


Review that system and be sure you understand it. y is the complement of x and w is the supplement of x. The equation using only the y and w is for the last part of the description.


Understood? If no, keep examening until you do; if yes, then: Solve the system.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

If half of the complement of a certain angle is 1° more than one-sixth of the supplement of the angle, find the angle.
Let angle be A

Then its complement is 90 - A, and its supplement is 180 - A

We then get: %281%2F2%29+%2A+%2890+-+A%29+=+%281%2F6%29+%2A+%28180+-+A%29+%2B+1

%2890+-+A%29%2F2+=+%28180+-+A%29%2F6+%2B+1

3(90 - A) = 180 - A + 6 ------ Multiplying by LCD, 6

270 - 3A = 186 - A

- 3A + A = 186 - 270

- 2A = - 84

A, or measure of angle = highlight_green%28matrix%281%2C3%2C+%28-+84%29%2F%28-+2%29%2C+or%2C+42%5Eo%29%29

It's that easy....nothing COMPLEX!!