HELP: SAT Geometry Question

<p>Line segments QW, QX, QY, and QZ are segments of differnt lines which intersect at point Q. Segments QX bisects <WQZ. If m<WQY=60, m<YQZ=30, and m<WQZ=90, what is the measure of <XQY?</p>

<p>A. 15
B. 30
C. 45
D. 60
E. 90</p>

<p>The answer is A, I feel this is more of a conceptual error on my part than anything else. PLEASE EXPLAIN how to arise at answer. I could not even draw a functional picture for this question. HELP</p>

<p>Ok, draw a right angle, and call it <WQZ. Then bisect the angle with a segment called QX. Note that <WQX and <XQZ are both 45 degrees. Then draw the segment QY so that <WQY=60. Since <XQY = <XQZ - <YQZ, we know that <XQZ is 45 degrees since segement XQ bisects the right angle and <YQZ is 30 since it is given in the problem. Thus, 45-30 = 15 = <XQY</p>

<p>Thank-you!!!</p>

<p>Just one additional question regarding your explanation. I thought <XQY=<XQZ+<YQZ? I think maybe I'm still drawing it wrong:(</p>

<p>NVM. I understand what I did. I never draw QY inside of <XQZ, your explanation cleared things out.</p>