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In the figure, , and both lines are intersected by transversal t. Complete the statements to prove that ∠2 and ∠8 are supplementary angles.

(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)

According to the Alternate Exterior Angles Theorem if a pair of Parallel lines are intersected by a transversal(t) then the alternate exterior angle are congurent.-Alternate Exterior Angles theorem and Linear Pair theorem

Step-by-step explanation:

Alternate exterior angles are said to be those angles  that are outside the "block" which is  formed by the parallel lines and are placed on the  opposite sides of the transversal(t)  

From the question we can say that both  ∠2 and ∠7 are outside the parallel lines and  ∠2 is on the right side of the transversal (t) and ∠7 is on the left side of the transversal. This makes ∠2 and ∠7  alternate exterior angles.

A linear pair is referred to as a pair of angles that are formed  from a straight line. When  ∠7 and ∠8 combined together they form a straight line this makes them a linear pair.

According to the  Alternate Exterior Angles Theorem if a pair of Parallel lines are intersected by a transversal(t) then the alternate exterior angle are congurent. Hence both Alternate Exterior Angles theorem and Linear Pair theorem is applicable