Question

What are the values of the variables?

I am confused of what I need to do. I'm not sure if I find both x and y, or y or x.

Should I also equal both of these equations to find the answer?

Answer 1

I know that:

$2x+12+3x+23=180$

How do I know that? Well, according to the Alternate Interior Angles Theorem, I know that 2x+12 could also go right above 3x+23.

If that is the case, then they would both equal 180° because they would both sit on a straight line. Let's solve:

$5x+35=180$

$5x=145$

$x=29$

Now we know what x is equal to. Let's solve for y. I know that:

$2x+12+y=180$

because they sit on a straight line. Since we have x, this is solvable. Let's plug in our x value and solve.

$2(29)+12+y=180$

$58+12+y=180$

$70+y=180$

$y=110$

Your final answers would be:

$x=29$

$y=110$

If you need to find the angles, just plug in these numbers for the variables and solve.