Hello!
I've altered the diagram and attached it below. I've added a circle; circles measure 360°. Segment CD is half the measure of the circle, thus it measures 180°. That means that if you add all the angle measures up, they have to equal 180°. Let's make an equation.
180 = (4x + 8) + 34 + (76 - x)
Now we can solve algebraically for x.
180 = 4x + 8 + 34 + 76 - x
180 = 3x + 118
62 = 3x
20.67 ≈ x
Answer:
x ≈ 20.67