Question

Find the value of x.........

Answer 1

The left triangle:
75 + 50 + x = 180
125 + x = 180
Subtract 125 from both sides.
x = 55 degrees

The center angle on the right triangle is also 55 degrees because the angles are vertical angles.

55 + 85 + x = 180
140 + x = 180
Subtract 140 from both sides.
x = 40 degrees

Answer 2

The angles of a triangle should add up to 180 degrees. in the left triangle, you should find the 3rd angle

75 + 50 + y = 180
125 + y = 180
y = 55

vertical angles are congruent, so the left angle on the right triangle will also be 55 degrees. 

then you do the same thing to find x.

85 + 55 + x = 180
140 + x = 180
x = 40