Question

What must be true for lines a and b to be parallel lines? Select four options.

Answer 1

A, B, G, and H are the correct answers.

I just took the quiz on edge

Answer 2

The question is missing figure and the options. So, the figure is attached alongwith the options

Answer:

Correct options: (1), (2) , (7) and (8)

Step-by-step explanation:

Given:

Lines a and b are parallel.

Consider a║b  and 'd' be a transversal  then,

Statements                                    Reasons

1. ∠BXZ = ∠AZP = 58°                Corresponding angles are equal

∴ m∠2 = 58°

2. ∠BYC = ∠XYZ = $(4x-10)$° Vertically opposite angles are equal

Now, consider a║b and 'c' be a transversal then,

Statements                             Reasons

1. ∠XYZ = ∠QZU = $(4x-10)$°  Corresponding angles are equal

∴ m∠1 =  $(4x-10)$°

2.∠PZA + ∠PZQ + ∠QZU = 180° Sum of angles on a straight line is 180°.

3. $58\° +(3x-1)\°+(4x-10)\° = 180\°$      Substitution property

4. $47\° + 7x= 180\°$                   Combining like terms

5. $7x=180\°-47\°$                         Subtraction property of equality

   ∴ $7x = 133\°$

6. $x = 19\°$                                 Division property of equality

Plug in $x = 19\ in\ (3x-1)\°\ and\ (4x-10)\°$, we get

$(3x-1)\° = (3(19)-1)\°$ = 56°

$(4x-10)\° = (4(19)-10)\°$ = 66°

So, $(3x-1)\° \ne (4x-10)\°$

Hence, options (1), (2) , (7) and (8) are correct.