PQ and RS are two lines that intersect at point T as shown b

PQ and RS are two lines that intersect at point T, as shown below: Which fact is used to prove that angle PTR is always equal to angle STQ? If two angles are equal to the same measure, then the angles are congruent. If two angles are equal to the same measure, then the angles are supplementary. Lines PQ and RS have a fixed length. Lines PQ and RS intersect at right angles.

Solution

Sum of angles PTR and PTS is equal to 180 degrees

PTR+PTS=180

This is equation 1

Sum of angles PTS amd STQ is equal to 180 degrees

PTS+STQ=180

This is equation 2

From above two equations

We can say that angle PTR=angle STQ

Therefore vertically opposite angles are equal

1st option