Question

PQ and RS are two lines that intersect at point T.

Which fact is used to prove that angle PTS is always equal to angle RTQ?

The sum of the measures of angles RTQ and QTS is equal to the sum of the measures of angles
QTS and PTS.

Angle RTQ and angle QTS are complementary angles.

The sum of the measures of angles RTQ and PTS is equal to the sum of the measures of angles RTP and QTS.

Angle RTQ and angle PTS are supplementary angles.

Answer 1

The sum of the measures of angles RTQ and QTS is equal to the sum of the measures of angles
QTS and PTS. I think this one is the corect answer :))

Answer 2

A.

Explanation:

We are given that two lines PQ and RS are intersect at point T.

We have to find the fact which is used to prove that angle PTS is always equal to angle RTQ.

We know that linear angles are supplementary and sum is 180 degrees

Therefore,
`\angle QTS+\angle PTS=180^(\circ)`

`\angle  QTS+\angle RTQ=180^(\circ)`

From both equation we get

`\angle QTS+\angle RTQ=\angle QTS+\angle PTS`

Cancel angle QTS on both sided the we get

`\angle RTQ=\angle PTS`

Hence, option A is true.

Therefore, when two lines are intersect then opposite angles are equal.