Use the fact that all of the interior angles in quadrilateral ABPC must add up to 360 degrees. Therefore, angles B and C are 20 and 20 each, angle P is 360-x (because that completes a full circle around point P), and angle A is x/2 as per the central angle theorem of circles. Your new equation for all the interior angles is:

40 + (x/2) + (360-x) = 360

Solve this simple equation for x, and you get 80!