Question

the bisectors of angle A and Angle B of a quadrilateral ABCD meet at a point O if angle C and angle D are 120 degree and 80 degree respectively find the measure of angle AOB ​

Answer 1

Answer:

We have,

ABCD is a quadrilateral.

Given that,

∠C=70

o

,∠D=50

o

So,

∠A+∠B+∠C+∠D=360

o

(A+B)=360

o

−(C+D)

⇒(A+B)=360

o

−(70

o

+50

o

)

⇒(A+B)=360

o

−120

o

⇒(A+B)=240

o

According to given question,

∠OAB=

2

∠A

∠OAB=

2

∠B

Now,

∠OAB+∠OBA=

2

∠A+∠B

=120

o

⇒∠AOB+120

o

=180

o

⇒∠AOB=180

o

−120

o

⇒∠AOB=60

o

Hence, this is the answer.