Question

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

Answer 1

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

$x=z$

$x+y=180\°$

Answer 2

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°.