Algebra solution for geometry problem

Okay, here's the problem. I'm supposed to find angles 1, 2 & 3. Where Angle 1=2x+40, Angle 2=2y+40 and Angle 3=x+2y. I can't figure out how to make an illustration for the problem, but it's 2 intersecting lines.

I know that Angles 1 & 2 = 180 and that angles 2 & 3 = 180, so I'm figuring:

180=(2x+40)+(2y+40) and
180=(2y+40)+(x+2y)

Also, I know that 2x+40=x+2y

No matter how I work on this problem, I can't isolate the variables to get an answer for x and y. Perhaps I'm going down the wrong path???

Can anyone help set me straight??? :shock:

okieopie said:

180=(2x+40)+(2y+40) and
180=(2y+40)+(x+2y)
2x+40=x+2y

Click to expand...

I don't know where you got these equations, so I really can't comment on their validity. I'm a little suspicious, but that won't stop us from solving the system. I'm a little worried that we have three (3) equations, but only two (2) variables. There may be NO solution.

Simplify
180 = (2x+40)+(2y+40) = 2x + 2y + 80
180 = (2y+40)+(x+2y) = x + 4y + 40
2x+40 = x+2y ==> x + 40 = 2y

Simplify some more
180 = 2x + 2y + 80 ==> 90 = x + y + 40
180=(2y+40)+(x+2y) = x + 4y + 40
x + 40 = 2y

Simplify some more
90 = x + y + 40 ==> 50 = x + y
180 = x + 4y + 40 ==> 140 = x + 4y
x + 40 = 2y

Here's what we have to work with.
50 = x + y
140 = x + 4y
x + 40 = 2y <== Solve one for x - just because it looks easy.

x = 2y - 40 <== Substitute this expression into the other two

50 = x + y ==> 50 = (2y - 40) + y ==> 50 = 3y - 40 ==> 90 = 3y ==> y = 30
140 = x + 4y ==> 140 = (2y - 40) + 4y ==> 180 = 6y ==> y = 30

We should feel blessed at this moment. y = 30 in both cases. We HAVE a solution!

You do the rest. What were you getting?

Okay, NOW I get it. I'm a little rusty on the algebra and didn't think about substituting the value of x with a y variable equation. Makes total sense. Thanks so much.

Using the same process for x, I get that

Y=50-x

So...
140 = x+4(50-x)
140 = x+200-4x
140 = 200 – 3x
-60 = -3x
20 = x

Checking it with the next equation...
x + 40 = 2(50 – x)
x + 40 = 100 – 2x
3x = 60
x = 20

Since y = 30 and x = 20, it's simple to see that Angle 1 = 2*20+40 = 80

Angle 2 = 2*30+40 = 100

Angle 3 = 20+(2*30) = 80

Thanks so much for the help!!! I'm a happy camper now. :lol:

If you need the practice, using the same process is a good idea. If you want to save time, just grab any convenient equation and find the other value with substantially greater ease. For example, x = 2y - 40, would have been a lot simpler.