First, you combine the equations in blue to be
-4x + 109 = 117

Now solve for x x=-2

And finally, substitute -2 in for x in the blue equations to get the angle's values. You can check your work by seeing if the values add up to 117 (which they do) :)

Now solve for x x=-2

And finally, substitute -2 in for x in the blue equations to get the angle's values. You can check your work by seeing if the values add up to 117 (which they do) :)