Question

Abcd is a rhombus such that angle acb =40 then angle adb is50

Answer 1

Given: ABCD is a rhombus. Diagonals bisect each other perpendicularly.  Hence ∠BOC = 90°. Given: ∠OCB = 40° AD||BC and BD is the transversal ∴ ∠ADB = ∠DBC (Alternate angles) Hence in right angled DBOC, ∠BOC + ∠OCB + ∠OBC = 180° ⇒ 90° + 40° + ∠OBC = 180°⇒130° + ∠OBC = 180° ⇒ ∠OBC = 180° - 130° = 50° But ∠OBC = ∠DBC. Therefore, ∠ADB = 50°