Question

Letters x, y, and z are angle measures. Which

equations would guarantee that lines p and q are
parallel? Check all that apply.

Z=x
x+y= 180°
x+z=180°
x=y
y +z = 180°
​

Answer 1

z=x

x+y= 180°

Explanation:

If two parallel lines are intersected by the same transversal,

Then,

• Alternative interior angles are equal.
• Alternative exterior angles are equal.

• Corresponding angles are equal

• Adjacent interior angles are supplementary.

If from these properties we have at least one information then we can say that lines are parallel,

Thus, if x = z ⇒ line p and q are parallel,

if x + z = 180° ⇒ line p and q are parallel.

Answer 2

• z=x
• x+y= 180°

Explanation:

The lines will be parallel if corresponding angles are congruent (z=x) or if adjacent interior angles are supplementary (x+y=180°).

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The other relations can be true without forcing the lines to be parallel.