50 points. 1. provide reasons for the proof. given: line p is parallel to line r. prove: ∠1 is supplementary to ∠7.

Given: Line p is parallel to line r.

Alternate exterior angles states that two angles in the exterior of the parallel lines, and on opposite sides of the transversal.

Alternate exterior angles are non-adjacent and congruent.

               [ Alternate exterior angles]

Since, Angles are congruent if they have the same angle measure in degrees

 ....[1]         [by definition of congruent Angles]

Linear pair states that a pair of adjacent angles formed when two lines intersect.

therefore, by definition   and forms a linear pair.

Since, linear pair are always supplementary.

is supplementary to

Supplementary angles states that two angles are supplementary that means they add up to measure 180 degree.

Substitute the equation [1] in above equation we get;

then, by the definition of supplementary angle ;

is supplementary to

a

step-by-step explanation: