Question

Alex is writing statements to prove that the sum of the measures of interior angles of triangle PQR is equal to 180°. Line m is parallel to line n.

Line n is parallel to line m. Triangle PQR has vertex P on line n and vertices Q and R on line m. Angle QPR is 80 degrees. Segment PQ makes 40 degrees angle with line n and segment PR makes 60 degrees angle with line n.

Which is a true statement he could write?

Angle PRQ measures 40°.
Angle PQR measures 60°.
Angle PRQ measures 80°.
Angle PQR measures 40°.

Answer 1

The stuff in pink is the stuff I found based on the information given. The pink 40 comes from the blue 40. The reason that both of those angles are congruent is because they are alternate interior angles. This is the same reason about the angles whose measurements are 60.

So the following things are true that we found that weren't already given:
Angle PQR is 40
Angle PRQ is 60

Answer 2

Thanks

Answer 3

No problem. Have a nice day.

Answer 4

You too