Question

Fill in the blank with the phrase that makes the proof statement true. Lines a and b are parallel. ________ because they form a linear pair. a. angle 1 is supplementary to angle 2 b. angle 1 is congruent to angle 3 c. angle 3 is supplementary to angle 2 d. angle 2 is congruent to angle 3

Answer 1

I have drawn the figure for you as well as represented different angles as 1,2,3,4.

You have written that  Lines a and b are parallel.

There are many reasons for that.

∠1+∠2=180°[ co-interior angles]

∠3 +∠4=180°[co-interior angles]

∠1 =∠3[alternate angles]

∠2 = ∠4[alternate angles]

∠1 = ∠7[corresponding angles]

∠4 =∠8[corresponding angles]

∠2 = ∠5[corresponding angles]

∠3 = ∠6[corresponding angles]

Out of many possibilities you have given

If angle 1 is supplementary to angle 2 i.e

∠1 + ∠2=180°

This is the Solution .

As Depicted in the diagram,(∠1,∠4),(∠5,∠6),(∠2,∠3),(∠7,∠8),(∠1,∠5),(∠4,∠6),(∠2,∠7)(∠3,∠8)  these angles form linear pair.Because the sum of each pair of angles is 180°.