In the figure a//b and both lines are intersected by transversal t. complete the statements to prove that and are supplementary angles.

The correct answers are:

Alternate Exterior Angles theorem and Linear Pair theorem.

Explanation:

Alternate exterior angles are ones that are outside the "block" formed by the parallel lines and on opposite sides of the transversal.  Both ∠2 and ∠7 are outside the parallel lines; additionally, ∠2 is on the right side of the transversal and ∠7 is on the left.  This makes them alternate exterior angles.

A linear pair is a pair of angles that form a straight line.  ∠7 and ∠8, when combined, form a straight line; this makes them a linear pair.

Hence, are supplementary angles as .

Explanation:

Given: and both lines are intersected by transversal .

From the figure,

                            (Given)

                      (Alternate Exterior opposite angles)

           (Linear pair property)

           (Co-exterior angles)

Here, are supplementary angles as sum of these two angles are equal to .

Therefore,   are supplementary angles as .

Hence proved.

Learn more about Parallel line and transversal line here:

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just get this app called photo math it should be able to do those