Question

 If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is​

Answer 1

Answer:

<AOB = (1/2)(<C + <D)

Step-by-step explanation:

In any quadrilateral, sum of its four angles = 360°

As such here in the quadrilateral ABCD also, <A + <B + <C + <D = 360°

==> <C + <D = 360° - (<A + <B)

2) Dividing the above by 2,

(1/2)(<C + <D) = 180° - (1/2)(<A + <B) ------- (i)

3) In the triangle AOB, <AOB = 180° - (1/2)*(<A + <B) ------- (ii) [Since given AO & Bo are bisectors of angles A & B respectively]

4) Thus from (i) & (ii) above,

<AOB = (1/2)(<C + <D)