Which statement is used to prove that angle ptr is always equal to angle stq?

lines pq and rs do not have a fixed length.

angle ptr and angle pts are supplementary angles.

lines pq and rs intersect at an angle less than a right angle.

angle ptr and angle pts are complementary angles.

The

first of all, the theorem says, vertical angles are congruent. that's why  Angle PTR and angle PTS are congruent.
according to the image, the true answer is Angle PTR and angle PTS are

complementary angles, that is because  mAngle PTR + m angle PTS are ≤90°

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle