Vertical angles are equal to each other based on the vertical angles theorem.
Since they are equal to each other, make them equal to each other in an equation.
Your equation should look like this: m∠3 = m∠4
Plug in the expressions for m∠3 and m∠4 in the equation. Now your equation should look like this:
(14x - 7) = (10x + 17)
Subtract 10x from both sides.
4x - 7 = 17
Add 7 to both sides.
4x = 24
Divide both sides by 4.
x = 6
Plug in 6 for x into m∠3.
14(6) - 7 = 84 - 7
84 - 7 = 77
m∠3 = 77°