Question

in parallelogram ABCD angle abd = 30 , angle adb = 40 . find angle adc and angle abc....bd transversal

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°

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Answer 2

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