Which fact is used to prove that angle PTR is always equal to angle STQ?

Question

anonymous · Answer

attachment

pooja195 · Answer

What kind of angles are the two angles forming?

anonymous · Answer

A) If two angles are equal to the same measure, then the angles are congruent
B) If two angles are equal to the same measure, then they are supplementry
C) Lines PQ and RS have a fixed length
D) Lines PQ and RS intersect at right angles

pooja195 · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @pooja195
What kind of angles are the two angles forming?
$\color{#0cbb34}{\text{End of Quote}}$

pooja195 · Answer

They are vertical angles...what does that mean?

anonymous · Answer

I have no clue ... ;/

pooja195 · Answer

Read this https://www.mathsisfun.com/geometry/vertical-angles.html

anonymous · Answer

ok got it .. a little better

pooja195 · Answer

Alright reading that you should be able to figure out the answer :)

anonymous · Answer

um no still dont know but thanks i guess

pooja195 · Answer

"Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each." This being from the example.
Back to the question, the arches tell us that the angles are equal to each other

pooja195 · Answer

Vertical angles are also congruent to each other 
So same measure and congruent match up with which one of your answer choices?