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