If m< 2= 7x + 7, m< 3= 5y, and m< 4 = 140, find the values of x and y.

Angles 1 & 3 have to be equal by the opposite angle theorem. Angles 2 & 4 also have to be equal because of this theorem. 

Therefore, you set 2 & 4 equal and solve for x.
7x + 7 = 140.
You should get x=19.

You now need to set 1 & 3 equal, but you aren't give angle 1.
You can find 1 because you know angle 1  + angle 2 = 180 degrees.

Therefore,
angle 1 is unknown (z)
angle 2 is equal to angle 4 which is 140 degrees.
140 + z = 180
z = 40 

Now you set angle 3 to angle 1:
5y = 40
y = 8

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