SOLUTION: Prove that the bisector of two adjacent supplementary angles include a right angle

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Question 1046706: Prove that the bisector of two adjacent supplementary angles include a right angle
Answer by MathLover1(20850) About Me  (Show Source):
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< AOC and < BOC are supplementary ...................given
rays OE and OD bisect < BOC+ and < AOC respectively
to prove: <+DOE=90°
proof:
.............statement........................-----------------..................reason
< AOC+%2B+BOC+=++180°..............................................given
rays OE and OD bisect < BOC+ and < AOC respectively....................given
%281%2F2%29+AOC+%2B+%281%2F2%29BOC+=+%281%2F2%29180°
%281%2F2%29AOC+%2B+%281%2F2%29BOC+=+90°
=> < DOC+=++%281%2F2%29AOC and < COE+=+%281%2F2%29BOC
=> < DOC+%2BCOE+=+90°......................OE and OD bisect < BOC+ and < AOC

=> < DOE+=+90°