Question

select the correct answer from each drop - down menu. in the figure, a || b, and both lines are intersected by transversal t. complete the statements to prove that ∠2 and ∠8 are supplementary angles. a || b (given) m∠2 = m∠7 ( ) m∠7 + m∠8 = 180° ( ) m∠2 + m∠8 = 180° (substitution property) ∠2 and ∠8 are supplementary (definition of supplementary angles)

Explanation:

Step1: Identify angle - pair relationship for m∠2 = m∠7

Since a || b, ∠2 and ∠7 are alternate - exterior angles. By the Alternate Exterior Angles Theorem, when two parallel lines are cut by a transversal, alternate exterior angles are congruent. So the reason for m∠2 = m∠7 is "Alternate Exterior Angles Theorem".

Step2: Identify angle - pair relationship for m∠7 + m∠8 = 180°

∠7 and ∠8 are a linear pair. By the Linear Pair Postulate, if two angles form a linear pair, then they are supplementary (their sum is 180°). So the reason for m∠7 + m∠8 = 180° is "Linear Pair Postulate".

Answer:

First blank: Alternate Exterior Angles Theorem
Second blank: Linear Pair Postulate