SOLUTION: Hi, I was wondering there is two lines that form a perpendicular line that looks like an x and the top angle says (x+y+5) the left angle says y and the right angle says 2x. y and x

Algebra ->  Points-lines-and-rays -> SOLUTION: Hi, I was wondering there is two lines that form a perpendicular line that looks like an x and the top angle says (x+y+5) the left angle says y and the right angle says 2x. y and x      Log On


   

Question 700143: Hi, I was wondering there is two lines that form a perpendicular line that looks like an x and the top angle says (x+y+5) the left angle says y and the right angle says 2x. y and x+y+5 are supplementary and x+y+5 and 2x are supplementary. I already wrote out 2y+x+5=180 and then 3x+y=5=180 but I don't know how to solve it from there.
Answer by KMST(5398) About Me  (Show Source):
You can put this solution on YOUR website!
You are right.
The angles measuring (in degrees) y and x%2By%2B5 are supplementary,
so y%2B%28x%2By%2B5%29=180 --> x%2B2y%2B5=180 as you wrote.
The angles measuring x%2By%2B5 and 2x are also supplementary,
so 2x%2B%28x%2By%2B5%29=180 --> 3x%2By%2B5=180 as you knew.
Those two equations can be simplified a bit.
x%2B2y%2B5=180 --> x%2B2y=180-5 --> x%2B2y=175
3x%2By%2B5=180 --> 3x%2By=180-5 --> 3x%2By=175
Then we would have the system of linear equations
system%28x%2B2y=175%2C3x%2By=175%29
The solution is highlight%28x=35%29 with highlight%28y=70%29
The three angle measures would be
highlight%28y=70%29 for the left angle,
2x=2%2A35=highlight%2870%29 for the right angle, and
x%2By%2B5=35%2B70%2B5=highlight%28110%29 for the top angle.

ALTERNATE WAYS TO THE SAME SOLUTION:
The left and right angles are vertical angles, so they have the same measure,
and y=2x could be one of your equations.
Then your system could be
system%28y=2x%2C3x%2By=175%29 or system%28x%2B2y=175%2Cy=2x%29