Prove angle 1 and angle 5 are supplementary.
Prove angle 8 and angle 4 are congruent

The answer is below

Step-by-step explanation:

a)

∠1 ≅ ∠4               When two parallel lines are cut by a Transversal, the pair    

                            of angles on the outer side of each of those two lines

                             but on opposite sides of the transversal are Alternate    

                             Exterior Angles which are equal.

∠1 = ∠4                   Definition of Alternate exterior angles.

∠4 and ∠5 form      Definition of linear pair.

linear pair

∠4 and ∠5 are         If linear pair, then it is supplementary.

supplementary.

m∠4 + m∠5 = 180     Definition of supplementary

m∠1 + m∠5 = 180      Substitution property of equality

∠1 and ∠5 are           Definition of supplementary.

supplementary.

b)

∠5 ≅ ∠2               When two parallel lines are cut by a Transversal, the

                             angles in matching corners are called corresponding

                             angles which are equal. These angles are congruent.

∠2 ≅ ∠4                When two parallel lines are cut by a Transversal, the

                             angles in opposite positions relative to a transversal

                             are alternate angles. These angles are congruent.

∠5 ≅ ∠4                 Substitution property of equality

∠5 ≅ ∠8                When two parallel lines are cut by a Transversal, the

                             angles in opposite positions relative to a transversal

                             are alternate angles. These angles are congruent.

∠5 ≅ ∠4                 Substitution property of equality

the answer is vanilla

step-by-step explanation: