Question

In the diagram below, P is circumscribed about quadrilateral ABCD. What is the value of x?

Answer 1

We know that
In any quadrilateral where the vertices are on the circumference of a circle, the opposite angles add up to $180$ degrees. 

So,
 in this problem
$(x+20) + 110 = 180 \\ x+130=180 \\ x=180-130 \\ x=50degrees$

therefore

the answer is
$x=50degrees$

Answer 2

When a quadrilateral is inscriptible the opposite angles are supplementary       
So:   A + C = 180°
X + 20° + 110° = 180°
Then:   
                X = 50°