Question

prove that the bisectors of two adjacent supplementary angles include a right angle

Answer 1

Let the measures of the two supplementary angles be x and y. By the definition of supplementary angles, 
x + y = 180° 

The angle between the bisectors will be 
x * 1/2 + y * 1/2, so it's 
(x + y) * 1/2 = 180°/2 = 90° 
which is a right angle. 

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Answer 2

Hey dear here is ur answer☜☆☞⌐╦╦═─
< 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
1/2AOC+1/2BOC=1/2180=+90°......................OE and OD bisect < BOC+ and < AOC

=> < DOE+=+90°
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