Question

HEY!! FRIENDS
........
IF ANY GENIUS IS HERE THAN HELP ME IN THIS QUESTION
( Question number 12 )
.... PLEASE MAKE ME BRAINLIST
♥️♥️♥️♥️

Answer 1

hey mate
refer to attachment

Answer 2

Answer:

⇒ ∠AOB = (1/2)[∠C + ∠D]

Step-by-step explanation:

From figure:

∠AO and ∠BO are bisectors of ∠A and ∠B respectively.

∴  ∠BAO = ∠A/2  ---- (i)

∴  ∠ABO = ∠B/2  ----- (ii)

We know that sum of angles of quadrilateral is 360°.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠C + ∠D = 360 - (∠A + ∠B)   ----- (iii)

In ΔAOB,

⇒ ∠BAO + ∠ABO + ∠AOB = 180°

⇒ ∠A/2 + ∠B/2 + ∠AOB = 180°

⇒ ∠AOB = 180 - ∠A/2 - ∠B/2

It can be written as,

⇒ ∠AOB = (360° - ∠A - ∠B)/2  {360/2 = 18}

⇒ ∠AOB = 360 - (∠A + ∠B)/2

⇒ ∠AOB = ∠C + ∠D/2  {From (iii)}

⇒ ∠AOB = (1/2) [∠C + ∠D]

Hope it helps!