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
Answers
Answered by
2
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.
Attachments:
Similar questions