Geometry: Help with this problem? Vertical angles & linear pairs

http://www.classzone.com/books/geometry/pdfs/g1_01_6ec.pdf


I need help with #8. I've been stuck on this problem for about 1 and a half hours! No matter how I try, I can never get the vertical angles to equal or for the linear pairs to equal to 180. Please help me!


Thankyou :)

We know three things:

(2x + 12y) = (8y - 4x).................as they are vertical angles
(2x + 12y) + (x + 2y) = 180.........as angles on a straight line add to 180
(8y - 4x) + (x + 2y) = 180............as angles on a straight line add to 180

So solve simultaneously:

(2x + 12y) = (8y - 4x)
6x = -4y
x = -(2/3)y

(2x + 12y) + (x + 2y) = 180
3x + 14y = 180
3 * [-(2/3)y] + 14y = 180
y = 180 / 12
y = 15
x = -10

You don't even need to use the third equation.