Answer:
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.
[tex]\angle 2 \cong \angle 7[/tex] [ Alternate exterior angles]
Since, Angles are congruent if they have the same angle measure in degrees
[tex]m \angle 2 =m\angle 7[/tex] ....[1] [by definition of congruent Angles]
Linear pair states that a pair of adjacent angles formed when two lines intersect.
therefore, by definition [tex]\angle 1[/tex] and [tex]\angle 2[/tex] forms a linear pair.
Since, linear pair are always supplementary.
[tex]\angle 1[/tex] is supplementary to [tex]\angle 2[/tex]
Supplementary angles states that two angles are supplementary that means they add up to measure 180 degree.
[tex]m\angle 1+m\angle 2 =180^{\circ}[/tex]
Substitute the equation [1] in above equation we get;
[tex]m\angle 1+m\angle 7 =180^{\circ}[/tex]
then, by the definition of supplementary angle ;
[tex]\angle 1[/tex] is supplementary to [tex]\angle 7[/tex]
