Question

given the figure, determine whether ( overline{wx}paralleloverline{yz} ).
a yes; there are two congruent right angles.
b no; ( mangle w + mangle z
eq180 )
c no; ( angle w ) and ( angle z ) are alternate interior angles but are not congruent.
d yes; ( angle x ) and ( angle y ) are congruent alternate inter angles.

Explanation:

Step1: Recall the property of parallel lines

If two lines are parallel, then consecutive interior angles are supplementary (sum to \(180^{\circ}\)). Here, if \(WX\parallel YZ\), then \(\angle W\) and \(\angle Z\) (consecutive interior angles) should satisfy \(m\angle W + m\angle Z=180^{\circ}\).

Step2: Calculate \(m\angle W + m\angle Z\)

Given \(m\angle W = 32^{\circ}\) and \(m\angle Z=35^{\circ}\), then \(m\angle W + m\angle Z=32^{\circ}+ 35^{\circ}=67^{\circ}
eq180^{\circ}\)

Answer:

B. No; \(m\angle W + m\angle Z
eq180\)