<p><a href="http://i1138.photobucket.com/albums/n523/FUAAARK/Math%20Problems/Problem15.png%5B/url%5D">http://i1138.photobucket.com/albums/n523/FUAAARK/Math%20Problems/Problem15.png</a>
In the figure above, 6 segments intersect at O; OD bisects AOF, OC bisects AOE, and OB bisects AOD. If x=40 and y=30, what is the measure of BOE?</p>
<p>Please give an explanation as to how you solved this problem. Thanks.</p>
<p>90 degrees. </p>
<p>AOB, which is angle x, has a measure of 40 degrees. Since OB bisects AOD, BOD has the same measure as AOB, 40 degrees.</p>
<p>Which means that AOD has a measure of 80 degrees. Since OD bisects AOF, DOF is also 80 degrees. Subtract the 30 degrees from that to get the measure of DOE, 50 degrees.</p>
<p>Since BOD and DOE together make BOE, add 40 to 50 to get 90 degrees.</p>
<p>Let me know if you need me to draw it out or something, because I’m getting confused typing this.</p>
<p>Before we begin you should know bisect means cut in half. So when it say’s bisect that means it cuts the original angle into two equal halves. </p>
<p>1) OB bisects AOD. We know A=40 so BOD= 40.
2) OD bisects AOF. We know AOD = 80 (from previous problem AOD=40 + BOD-40, so it is 80 altogether) so DOF= 80.
3) Since we know DOF= DOE+EOF then DOE+30(which is y)=80. Subtract 30 from both sides to get DOE=50.
4) DOE+BOD= BOE. So lets substitute them with their degrees to get 50+40=90.</p>
<p>So 90 is your answer, not sure if I did a good job at explaining though.</p>
<p>Edit: typed all that for nothing :(</p>
