Question

50 Points.

1. Provide reasons for the proof.
Given: Line p is parallel to line r.
Prove: ∠1 is supplementary to ∠7.

Answer 1

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.

`\angle 2 \cong \angle 7` [ Alternate exterior angles]

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

`m \angle 2 =m\angle 7` ....[1] [by definition of congruent Angles]

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

therefore, by definition
`\angle 1` and
`\angle 2` forms a linear pair.

Since, linear pair are always supplementary.

`\angle 1` is supplementary to
`\angle 2`

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

`m\angle 1+m\angle 2 =180^(\circ)`

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

`m\angle 1+m\angle 7 =180^(\circ)`

then, by the definition of supplementary angle ;

`\angle 1` is supplementary to
`\angle 7`