<p>I'm stumped on how you'd solve this geometry problem from the original blue book. It's test #4, section 3, page 656, #14.</p>
<ol>
<li>In the figure above, m||n and l bisects angle ABC. If 45 < y <55, what is one possible value of x?</li>
</ol>
<p>If a line segment intersects 2 parallel lines, congruent angles are formed. In this case, the measure of angle y is equal to the measure of angle ABC.</p>
<p>Since L bisects ABC, it cuts the the angle ABC in half. So, the measure of angle LBC is HALF the measure of angle y.</p>
<p>45 < y < 55
22.5 < LBC < 27.5</p>
<p>The corresponding angle of LBC along the other parallel line is congruent to LBC. The angle OPPOSITE that angle is x, which is a vertical angle, so that is also congruent.</p>
<p>Therefore, x is congruent to LBC, whose measure is in turn half the measure of y.</p>
<p>22.5 < x < 27.5 (the value of x can be any number between 22.5 and 27.5)</p>
<p>Thanks! I completely forgot that “bisects” means “cuts in half.” I thought it just meant intersects. Now I feel stupid…</p>