in parallelogram abcd of the given figure , angle dab = 60 degree and angle dbc = 80 degree .find angle abd.
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The angle ABD = 40°.
- Given quadrilateral ABCD , ∠DAB = 60° and ∠DBC = 80°.
- Now we have to find the angle of ABD.
- In triangle ABD and triangle CBD,
AD || BC (opposite angles of the parallelogram are parallel)
∠ACB = ∠CBD (Alternate angles)
∴ ∠ACB = 80°.
- Now, in ΔDAB,
∠A + ∠ADB +∠ABD = 180° (Sum of all angles of a triangle)
60° + 80° + ∠ABD = 180°
∠ABD = 180° - (60° + 80°)
∠ABD = 180° - (140°) = 40°
- Therefore, ∠ABD = 40°
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