Question

What must be true for lines a and b to be parallel lines? Check all that apply.

Answer 1

Answer:

Option (1), (2) , (7) and (8) is correct.

Step-by-step explanation:

Given: a║b  and d and c be transversal , We have to find the value of x and measure of angle 1 and 2.

Since, a║b  and d be a transversal  then ,

∠BXZ = ∠AZP = 58° ( corresponding angles )

Thus, m∠2 = 58°

∠BYC = ∠XYZ = (4X-10)° (vertically opposite angles)

Since, a║b  and c be a transversal  then,

  ∠XYZ = ∠QZU = (4X-10)°  (Corresponding angles)

Thus, m∠1 =  (4X-10)°

Also, Since, 'a' is a straight line.

Sum of angles on a straight line is 180°.

⇒ ∠PZA + ∠PZQ + ∠QZU = 180°

⇒ 58° +(3X-1)°+(4X-10)° = 180°

⇒ 58° + 7x - 11 = 180°

⇒ 47° + 7x  = 180°

⇒  7x  = 180°- 47°

⇒  7x  = 133°

⇒  x  = 19°

Put x = 19 in (3X-1)° and (4X-10)° , we get

(3X-1)° = (3(19)-1)° = 56°

(4X-10)° = (4(19)-10)°= 66

Thus, (3X-1)° ≠ (4X-10)°

Thus, option (1), (2) , (7) and (8) is correct.

Answer 2

I think I got most of it.