Question

ABCD is a quadrilateral and bro are the angle bisectors of angle A and B which meet at O if angle C is equal to 70 degree angle equal to 50 degree find angle

Answer 1

angle AOB is equal to 60°

Answer 2

let ∠OAB be 1 
∠OBA be 2
∠AOB be 3

∠A+∠B+∠C+∠D = 360

∠1+∠2+∠3= 180................(b)

$\frac{1}{2}$ (∠A+∠B+∠C+∠D) = 180 ...............(a)

now equate them both                                [ ∠A = 2∠1 ]  { ∠B = 2∠2 }

$\frac{1}{2}$ (∠A+∠B+∠C+∠D) = ∠1+∠2+∠3

2∠1+2∠2+∠C+∠D = 2∠1+ 2∠2+ 2∠3

∠C+∠D = 2∠3                                         ( ∠C= 70 and ∠D = 50 )

70 +50 = 2∠3

$\frac{120}{2} =$ ∠3                       [ ∠AOB = ∠3 ]

60° = ∠AOB