Question

If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is
(a) ∠C + ∠D
(b) 21 (∠C + ∠D)
(c) C D213+ + 1 +
(d) C D312+ + 1 +

Answer 1

ABCD is quadrilateral so, ∠A + ∠B + ∠C + ∠D = 360°
dividing by 2 both sides,
1/2(∠A ) + 1/2(∠B) + 1/2(∠C) + 1/2(∠D) = 180°
so, 1/2(∠C + ∠D) = 180° - 1/2(∠A) - 1/2(∠B)----(1)

now, according to question,
bisectors of ∠A and ∠B of quadrilateral ABCD meet at point O.
so, AOB is formed triangle in which ∠OAB = 1/2(∠A) and ∠OBA = 1/2(∠B)

also, ∠OAB + ∠OBA + ∠AOB = 180°
so, 1/2(∠A) + 1/2(∠B) + ∠AOB = 180°
∠AOB = 180° - 1/2(∠A) -1/2(∠B)
now, from equation (1),
∠AOB = 1/2(∠C + ∠D)

hence, option (b) is correct.
[note :- in question , you did mistake in typing, option (b) will be 1/2(∠C + ∠D)]