Question

Pls solve this question with all the steps

Answer 1

Step-by-step explanation:

From figure:

In ΔAOB & ΔCOB,

OA = OC

AB = BC {Since ABCD is a rhombus}

OB = OB

∴ ΔAOB ≅ ΔCOB

⇒ ∠AOB = ∠BOC   ----- (i)

∴ ΔAOD ≅ ΔCOD

⇒ ∠AOD = ∠COD   ----- (ii)

Now,

⇒ ∠AOB + ∠BOC + ∠COD + ∠AOD = 360°

⇒ ∠BOC + ∠BOC + ∠COD + ∠COD = 360° {From (i),(ii)}

⇒ 2∠BOC + 2∠COD = 360°

⇒ ∠BOC + ∠COD = 360°/2

⇒ ∠BOC + ∠COD = 180°

⇒ ∠DOB = 180°

Therefore, DOB is a straight line.

Hope it helps!