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

The correct phrase to fill in the blank is 'Angle 1 is supplementary to angle 2' because they form a linear pair when lines a and b are parallel.

Step-by-step explanation:

Lines a and b are parallel. Angle 1 is supplementary to angle 2 because they form a linear pair. The correct phrase to fill in the blank is option a.

When two lines are parallel and are cut by a transversal, the angles that form a linear pair with the angles on the transversal are supplementary, meaning they add up to 180 degrees. This is consistent with the concept that parallel lines never intersect, and thus the lines adjacent to the transversal must add up to 180 degrees to maintain the parallel nature.

Answer 2

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°.