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
1 answer:
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°.
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