Can someone help with this Geometry problem?

Question

I really don't get it and I've been trying it for a LONG time.

some help please, not just the answer would be VERY appreciated.

THANK YOU! =D

http://i212.photobucket.com/albums/cc136/DreaxLuvsXu/geometry.jpg

Answer 1

m/1 = m/3 by the Vertical Angles Theorem.

Thus:

2*x + 40 = x + 2*y

2*y = x + 40

We can not replace 2*y in m/2

m/2 = x + 80

Now we have reduced the original system to:

m/1 = 2*x + 40

m/2 = x + 80

We also know by the Vertical Angles Theorem that:

2*m/1 + 2*m/2 = 360°

2(2*x + 40) + 2(x + 80) = 360°

Now we solve for x

6*x+240 = 360

x = (360-240)/6 = 20

Thus m/1 = 2(20) + 40 = 80

m/1 = 80 = m/3 = 20 + 2*y

y = (80-20)/2 = 30

m/2 = 2(30)+40 = 100

Thus m/1 = m/3 = 80°  and m/2 = 100°