sat-dog

Choice A is correct. It’s given that WZ and XY intersect at point Q. It follows that + + WQX and YQZ are vertical angles, which means they are congruent to each + + other. The figure shows that W and Y both have a measure of a°, so they are 3 3 congruent to each other. Therefore, QWX and QYZ are similar triangles, where WQ corresponds to YQ and WX corresponds to YZ. Since the lengths of YZ =WX corresponding sides in similar triangles are proportional, it follows that . YQ WQ =21 =70 =60 21 70 It’s given that YQ , WQ , and WX . Substituting for YQ, for WQ, 60 6 60 YZ =WX YZ= YZ= and for WX in the equation yields 21 70, or 21 7. Multiplying each YQ WQ 21 =18 18 side of this equation by yields YZ . Therefore, the length of YZ is . Choice B is incorrect. This is the length of QZ, not YZ. Choice C is incorrect. This is the length of XQ, not YZ. Choice D is incorrect and may result from conceptual or calculation errors.