Question

ABCD is a rhombus
If angle ACB=40 ,Find angle ADB​

Answer 1

Answer:

50°

In given figure ABCD is a rhombus. We know that diagonals of rhombus bisect each other perpendicularly.

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)

Answer 2

Answer:

AD|| BC

angle DAC = angle BCA =40°

angle AOD =90°

angle ADO + angle BCA + angle OAD = 180°

angle ADO +40° +90°= 180°

angle ADO +130°=180°

angle ADO=180°-130°

angle ADO=50°