Finding the angles in an isosceles trapezoid

[burt]

I was given the following picture (I will attach it below) with the following instructions:

PQRS is an isosceles trapezoid. If angle TRS=100 degrees, angle T=35 degrees, and PS=TS, find the measures of the numbered angles.

As you can see in the attached picture, TRS and angle T are outside of the trapezoid. I do not see how to solve this. I see that angle PRS is 80 degrees but I have not yet gotten further than that. I also don’t understand the significance of PS=TS. It does not seem to be making the triangles congruent, because in that case angle PRS would be 100 degrees not 80 - and it can’t be both. Any ideas?

 

[pka]

I agree. the given data lead to contradictions. The drawn diagram seems to be misleading.

 

[burt]

I agree. the given data lead to contradictions. The drawn diagram seems to be misleading.

I’m thinking the key lies in the fact that triangle PTS is isosceles.

 

[pka]

I’m thinking the key lies in the fact that triangle PTS is isosceles.

I agree, that seems too odd.

 

[burt]

I agree, that seems too odd.

I think this answer is correct:

 

[Dr.Peterson]

Yes, that is correct.

I don't see why there would be any contradictions; drawings "not to scale" are typical of such a problem, and the first thing to do is to resketch the drawing to make it a little less misleading, then mark up any facts you see. The isosceles triangle is indeed the key.