As you noted, ∠PRS=80°. Take the triangle △TRS: we know two angles out of three, so that ∠TSR=45°. Now take the isosceles triangle △PTS: the two angles adjacent to the base PT are equal to 35°, so the third angle ∠PST=110° and then ∠PSR=65°. This is one of the two angles adjacent to the base of an isosceles trapezoid: knowing it, you can easily complete the solution.
All angles in a trapezoid add up to 369. In the isoceles trapezoid, non- adjacent angles are supplementary and angles on the same side are equal to each other.
