Question

Find the measures of the numbered angles in the isosceles triangle

Answer 1

Ange 1 is 52, Angle 2 is 128, Angle 3 is 128

Explanation:

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.

Answer 2

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.