In the adjoining figure, $$AB$$ || $$DC$$. Also, $$PG=PF$$. The measure of angle $$x$$ in degrees is

Since $$AB$$ is parallel to $$DC$$ and $$\angle ABC=142^\circ$$, the acute angle between the two intersecting directions at $$C$$ is $$38^\circ$$. The two marked right angles in quadrilateral $$CEPJ$$ then give $$\angle EPJ=142^\circ$$. This is vertically opposite to $$\angle GPF$$, so the vertex angle of isosceles triangle $$GPF$$ is $$142^\circ$$. Each base angle is $$19^\circ$$, and the exterior angle marked $$x$$ is $$180^\circ-19^\circ=161^\circ$$.