Answer is x = 11
Your equation since they are vertical angles, they are equal to each other
8x + 7 = 9x - 4
Subtract 9x from both sides to combine variable
8x -9x +7 = 9x - 9x -4
Combine
-1x +7 = -4
Subtract 7 from both sides to solve for x
-x +7 -7 = -4 -7
Combine
-x = -11
x = 11
Substitute 11 for x in your angle expressions
8x + 7 = 9x - 4
8(11) + 7 = 9(11) - 4
88 + 7 = 99 - 4
95 = 95
They equal so it checks true
Problem solved