Assuming you want the value of x:
The angles are on a straight line which means they must add up to 180 degrees. Make this into an equation.
(4x - 10) + (7x - 8) = 180
Combine like terms.
11x - 18 = 180
Add 18 to both sides.
11x = 198
Divide both sides by 11.
x = 18
If you want the measurements of the angles, plug x into the angles.
4x - 10 ⇒ 4(18) - 10 = 62°
7x - 8 ⇒ 7(18) - 8 = 118°