By setting up the equation m∠VUC + m∠CUT = m∠VUT we can see that x = 8.
How to find the value of x?
We know that:
m∠VUC = -4 + 5x
m∠CUT = 140°
m∠VUT = 23x - 8
Notice that we must have that:
m∠VUC + m∠CUT = m∠VUT
Then we can write the equation:
-4 + 5x + 140 = 23x - 8
Let's solve this for x:
5x + 136 = 23x - 8
136 + 8 = 23x - 5x
144 = 18x
144/18 = x
8 = x