Question

ABCD is a rhombus such that angle ACB=40 then find the value of angle ADB​

Answer 1

Answer:

50°

Step-by-step explanation:

ABCD is a rhombus. We know that diagonals of rhombus bisect each other perpendicularly. Let the point of bisect be O.

Hence, ∠BOC= 90°

∠OCB = 40° (Given)

AD∥BC and BD is the transversal --- (Opposite sides of rhombus are parallel to each other)

∴ ∠ADB = ∠DBC ---- (Alternate angles)

In △OBC,

∠BOC + ∠OCB + ∠OBC = 180°

⇒ 90° + 40° + ∠OBC = 180°

⇒ ∠OBC =180° - 130°

∴ ∠OBC = 50°

But ∠OBC =∠DBC

∴ ∠ADB = 50° ---( Alternate angle)