SOLUTION: A supplement of an angle has a measure of 20 more than three times its complement. Find the measure of the angle. (The original angle.)

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Question 1203921: A supplement of an angle has a measure of 20 more than three times its complement. Find the measure of the angle. (The original angle.)
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
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When the problem is worded this way, it is ambiguous.

It is ambiguous, because it is unclear, who is "its complement":

        is it the complement to the "an angle", or to the "supplement of an angle".


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Comment from student : The complement is a complement to the an angle


My response : How do you know, which interpretation to use ?

Because it is YOU who composes these "problems" ?


        Unhappy are those students who receive
        such assignments from their “teachers”.



Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
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A supplement of an angle has a measure of 20 more than three times its complement.
Find the measure of the angle. (The original angle.)
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180-x, to be "a supplement of an angle x"

The description is potentially not clear.
Maybe to mean this: 180-x=20%2B3%2890-%28180-x%29%29.
Solve and see what happens.
180-x=20%2B3%28x-90%29
180-x=20%2B3x-270
180-20%2B270=4x
4x=430
x=107.5%2Adegrees-----------maybe. In fact, this is not a complement of any angle!

If that is not what you hoped for then maybe you could make the correct change to the problem description.

Maybe you meant for this: 180-x=20%2B3%2890-x%29.
180-x=20%2B270-3x
3x-x=20%2B270-180
2x=110
x=55%2Adegrees-------------this would make more sense.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
A supplement of an angle has a measure of 20 more than three times its complement. Find the measure of the angle. (The original angle.)

Let angle be A
Supplement of the angle: 180 - A
Complement of the angle: 90 - A
We then get: 180 - A = 3(90 - A) + 20
             180 - A = 270 - 3A + 20 
            - A + 3A = 270 + 20 - 180
                  2A = 110
Measure of the angle, or