Question

50 Points.

Answer 1

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.

$\angle 2 \cong \angle 7$                [ 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 $\angle 7$