Question

ABCD is a quadrilateral. AO and BO are the angle bisectors of angle A
and B which meet at O. If ZC = 70°, ZD = 50°, find ZAOB.​

Answer 1

Answer:

ANSWER

We have,

ABCD is a quadrilateral.

Given that,  

∠C=70  ,∠D=50  

So, ∠A+∠B+∠C+∠D=360  

(A+B)=360 −(C+D)

⇒(A+B)=360  −(70) +50)

⇒(A+B)=360   −120  

⇒(A+B)=240  

According to given question,

∠OAB=  2 ∠A

∠OAB=  2 ∠B  

Now,

∠OAB+∠OBA=  2

∠A+∠B  =120  

⇒∠AOB+120=180

 ⇒∠AOB=180    −120  ⇒∠AOB=60  

Hence, this is the answer.

Hope this helps!