What is the value of angle vux

There are two ways to do this.

The quicker way is to use the remote interior angle theorem. We have the interior angles 53 and 103 which add to 53+103 = 156 which is exactly the exterior angle VUX.

The slightly longer way involves finding angle TUV first. Let's say this is equal to the variable y

Adding any three interior angles of a triangle always gets us 180

53+103+y = 180

y+156 = 180

y = 180-156

y = 24

Angle TUV is 24 degrees

The angle supplementary and adjacent to this is angle VUX, which I'll call z

z+y = 180

z = 180-y

z = 180-24

z = 156

So this is another way to get to the answer 156 degrees.