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

Algebra ->  Geometry-proofs -> 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      Log On


   

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) About Me  (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