Question

AOB IS LINE, od bisect angle AOC and OE bisect angle BOC show that angle DOE is right angle

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Answer 1

mate here is your short answer very easy

see

OD is bisector of AOC

therefore, angle AOD = DOC

and similarly

OE is bisector of BOC

therefore,angle COE = EOB

Now

let,

angle AOD = A , DOC = B , COE = C and EOB = D

and, A = B and C = D ( because OD and OE are angle bisectors)

therefore,

we know that,sum of all interior angles is 180°

So,

AOD + DOC + COE + EOB = 180°

A + B + C + D = 180°

A + A + B + B = 180°

2A + 2B = 180°

2 ( A+B ) = 180°

A + B = 180° / 2

A + B = 90°

DOC + COE = 90°

DOE = 90°