Question 904683
{{{drawing( 400, 300, -10, 10, -10, 10,
line(-5,7,5,-7),
line(-5,-7,5,7),
locate(-0.5,2.5,y+x),
locate(1.5,0,y-x),
locate(-2.5,0,2x)

  )}}}

I think this is what you mean??
OK, when you look at the pairs of angles, you have two types of angles: linear pairs and vertical angles. 
Linear pairs sum to 180 degrees.
Vertical angles are congruent (same measure).
In your diagram, the linear pairs are:
{{{2x}}} and {{{y+x}}}
{{{y+x}}} and {{{y-x}}}
The vertical angles are : 
{{{2x}}} and {{{y-x}}}
So let's build equations using this information.

1.{{{2x+(y+x)=180}}}
1.{{{3x+y=180}}}


2.{{{(y+x)+(y-x)=180}}}
2.{{{2y=180}}}
2.{{{highlight(y=90)}}}


3.{{{2x=y-x}}}
3.{{{3x-y=0}}}


Since eq. 2 solved for {{{y}}}, you can use either 1 or 3 to solve for {{{x}}}. You could also add eq. 1 and eq. 3,

{{{3x+y+(3x-y)=180}}}
{{{6x=180}}}
{{{highlight(x=30)}}}


So the three angles, given clockwise, are {{{2x=60}}}, {{{y+x=120}}} degrees, and {{{y-x=60}}} degrees.

{{{drawing( 400, 300, -10, 10, -10, 10,
line(-5,7,5,-7),
line(-5,-7,5,7),
locate(-0.5,2.5,120),
locate(1.5,0,60),
locate(-2.5,0,60)

  )}}}