Question

In the given figure, ABCD is a quadrilateral and OD and OA are bisectors of ∠Dand ∠A. Find the value of ′x ′​

Answer 1

Step-by-step explanation:

We have,

ABCD is a quadrilateral.

Given that,

∠C=70o,∠D=50o

So,

∠A+∠B+∠C+∠D=360o

(A+B)=360o−(C+D)

⇒(A+B)=360o−(70o+50o)

⇒(A+B)=360o−120o

⇒(A+B)=240o

According to given question,

∠OAB=2∠A

∠OAB=2∠B

Now,

∠OAB+∠OBA=2∠A+∠B=120o

⇒∠AOB+120o=180o

⇒∠AOB=180o−120o

⇒∠AOB=60o