SOLUTION: Given: Angle AOC and angle COB form a linear pair. Ray OD and ray OE are the angle bisectors of the angles in the linear pair. Prove: Measurement andgle DOE = 90 degrees

Question 189691: Given:
Angle AOC and angle COB form a linear pair.
Ray OD and ray OE are the angle bisectors of the angles in the linear pair.
Prove:
Measurement andgle DOE = 90 degrees
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
Draw a pic to see what's happening

1. AOC+COB=180 ...................... Given (linear pairs add to 180)
2. AOD+DOC+COE+EOB=180 ..... Break up angles (the drawing helps)
3. DOC+DOC+COE+COE=180 ..... Substitute
4. 2*DOC+2*COE=180 ......... Combine terms
5. 2(DOC+COE)=180 .......... Factor
6. DOC+COE=90 .............. Divide
7. DOE=90 .................. Add angles
RELATED QUESTIONS
Given: angle AOC and angle COB are a linear pair. Prove: angle AOC and angle COB are a... (answered by solver91311)

True or false? If Ray AB intersects Ray CD in point E, then angle AED and angle BED form... (answered by tran3209)

Angle AOB and angle AOC are complementary angles. What is the measure of angle AOB if the (answered by ikleyn)

Ray MP bisects angle LMN. Ray MQ bisects angle LMP, and ray MR bisects angle QMP. If... (answered by Theo)

Two angles, angle 1 and angle 2, form a linear pair. The measure of angle 1 is twenty-two (answered by josgarithmetic)

Angle T and Angle U form a linear pair. If Angle T is eight more than Angle U find the... (answered by solver91311)

having trouble solving proof problems. page 71 #10 WRITE A PROOF ANGLE ABC IS CONGRUENT (answered by venugopalramana)

Angle PQR and Angle SQR form a linear pair. Find the sum of their... (answered by stanbon)

if angle 2 and angle 3 are suplementary angles, then angle 2 and angle 3 form a linear... (answered by cleomenius)