Question

INA QUADRILATERAL ABCD, AO & BO ARE BISECTORS OF ANGLE A & B RESPECTIVELY. PROVE THAT ANGLE AOB=1/2(ANGLE C+ ANGLE D)


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Answer 1

Step-by-step explanation:

We know angle A+angle B +angle C+ angle D=360              (1)

In triangle ABO  angle AOB+ 1/2(angle A+angle B)=180                                      

                                   2(AOB+ 1/2(angle A+angle B)=360      (2)

We have  angle   2 AOB + angle A+ angle B = angle A + angle B +angle C+ angle D

                This gives                       angle AOB= (angle C + angle D)/2

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Answer 2

We know angle A+angle B +angle C+ angle D=360              (1)

In triangle ABO  angle AOB+ 1/2(angle A+angle B)=180                                      

                                    2(AOB+ 1/2(angle A+angle B)=360      (2)

We have  angle   2 AOB + angle A+ angle B = angle A + angle B +angle C+ angle D

                 This gives                       angle AOB= (angle C + angle D)/2

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