Question

Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? Check all that apply

x = z


x + y = 180°


x + z = 180°


x = y


y + z = 180

Answer 1

Answer: The correct options are

(A) x = z.

(B) x + y = 180°.

Step-by-step explanation: Given that the letters x, y and z are angle measures.

We are to select the correct equations that would guarantee that lines p and q are parallel.

Since the lines p and q are parallel, so

(i) the angles with measures x and y are interior angles on the same side of the transversal

and

(ii) the angles with measure x and z are corresponding angles.

We know that

if two parallel lines are cut by a transversal, then the measures of the corresponding angles are equal

and

the sum of the measures of the interior angles on the same side of the transversal is 180°.

Therefore,

x + y =180°, since they are interior angles on the same side of the transversal

and

x = z, since they are corresponding angles.

Thus, the correct options are

(A) x = z.

(B) x + y = 180°.

Answer 2

we know that

If lines p and q are parallel

then

`x=z`---------> by corresponding angles

`x+y=180\°` -------> by consecutive interior angles

Let's verify all the equations to determine the solution to the problem.

Equations

case A)
`x=z`

The equation guarantees that the lines p and q are parallel (see the procedure)

case B)
`x+y=180\°`

The equation guarantees that the lines p and q are parallel (see the procedure)

case C)
`x+z=180\°`

The equation does not guarantee that the lines p and q are parallel. The only way would be that x-angle and z-angle are right angles

case D)
`x=y`

The equation does not guarantee that the lines p and q are parallel. The only way would be that x-angle and y-angle are right angles

case E)
`y+z=180\°`

The equation is always true, but toes not guarantee that the lines p and q are parallel.

therefore

the answer is

`x=z`

`x+y=180\°`