Question

PQ and RS are two lines that intersect at point T, as shown below:

Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent.

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

A - Lines PQ and RS do not have a fixed length.
B - Angle PTR and angle PTS are supplementary angles.
C - Lines PQ and RS intersect at an angle less than a right angle.
D - Angle PTR and angle PTS are complementary angles.

Answer 1

Option B - Angle PTR and angle PTS are supplementary angles

Explanation:

we know that

m∠PTR=m∠STQ -----> by vertical angles

we have that

The sum of angles PTR and PTS is always equal to 180 degrees, because are supplementary angles

so

m∠PTR+m∠PTS=180° ------> by supplementary angles