Answer:
x = 8
m∠V = 89°
What We Know
m∠W = 90°
m∠V = 11x + 1
m∠U = 12x + 10
m∠X = 75
The sum of all the angles in a quadrilateral is 360°
Solve For X
m∠W + m∠V + m∠U + m∠X = 360°
Plug what you know into the above equation in the appropriate spots
90 + (11x + 1) + (12x + 10) + 75 = 360
Combine like terms
90 + 11x + 1 + 12x + 10 + 75 = 360
176 + 11x + 12x = 360
176 + 11x + 12x = 360
176 + 23x = 360
23x = 184
Isolate x
x = 8
Find m∠V
Given: m∠V = 11x + 1
Plug in the x you previously found into the equation above and solve
m∠V = 11(8) + 1
m∠V = 88 + 1
m∠V = 89°