Bunuel wrote:

Lines m and n, shown above, are not parallel. Which of the following could be true?

(A) u = x

(B) u = y

(C) t = z

(D) w = y

(E) w + x = 180

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IF the lines are parallel, then these angles will be congruent (equal): alternate interior, alternate exterior, and corresponding. In addition, same-side interior angles and same-side exterior angles will be supplementary (=180).

The converse of all those properties is also true. For example, if two lines are cut by another line, and corresponding angles are congruent, the lines transversed are parallel.

Check each answer choice as if the lines were parallel, and discern whether choices would be true if lines were parallel, because we need the answer that is consistent with lines that are not.

It helps me to sketch same figure WITH parallel lines.

(A) u = x. If the lines were parallel, u and x would be corresponding angles, and hence congruent. Cannot be true (b/c if congruent, lines would be parallel).

(B) u = y. If the lines were parallel, u would = x, x+y is 180, so u+y would = 180, or u = 180 - y. Here they are equal, so lines are not parallel. Can be true.

(C) t = z. Same as A. If parallel lines, t and x would be congruent corresponding angles. Cannot be true.

(D) w = y. If parallel lines, w and y would be congruent alternate exterior angles. Cannot be true.

(E) w + x = 180. If parallel lines, x = t (alternate interior). On a straight line, w + t = 180. So w + x would equal 180. Cannot be true.

Answer B

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