Answer:
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
