SOLUTION: the measurement of angle 1 =2x+40 the measurement of angle 2 =2y+40 the measurement of angle 3 =x+2y And there is a picture that looks roughly like this: ('e's are used to prov

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Question 557102: the measurement of angle 1 =2x+40
the measurement of angle 2 =2y+40
the measurement of angle 3 =x+2y
And there is a picture that looks roughly like this:
('e's are used to provide correct spacing
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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Angles 1 and 3 are vertical to each other; angle 2 is supplementary to 1 and to 3.
2x%2B40=x%2B2y (angles 1 and 3 have the same measure)
%282x%2B40%29%2B%282y%2B40%29=180 (measures of angles 1 and 2 add to 180°)
%282y%2B40%29%2B%28x%2B2y%29=180 (measures of angles 2 and 3 add to 180°)
That gives you 3 equations on 2 variables.
Let's simplify:
2x%2B40=x%2B2y --> x-2y=-40
%282x%2B40%29%2B%282y%2B40%29=180 --> 2x%2B2y%2B80=180 --> 2x%2B2y=100 --> x%2By=50
%282y%2B40%29%2B%28x%2B2y%29=180 --> x%2B4y%2B40=180 --> x%2B4y=140
With two of the equations we may find a solution, which we would need to substitute in the other equation to see that it verifies.
If we take the system
x%2By=50
x%2B4y=140
subtracting the first equation from the second, we get
3y=90 --> y=30
and substituting into the first equation we get
x%2B30=50 --> x=20
If x=20 with y=30 satisfies x-2y=-40, then (x,y)=(20,30) is the solution. If not, there is no solution.
With x=20 and y=30, x-2y=20-2%2A30=20-60=-40, so (20,30)
(or x=20 with y=30 ) is the solution.