If ABCD is a parallelogram and BD its diagonal, find the sum of ABD and ADB if DCB and ABC are in the ratio 2 : 7.
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Given : ABCD is a parallelogram and BD its diagonal
Angles DCB and ABC are in the ratio 2 : 7.
To Find : sum of angles ABD and ADB
Solution:
DCB and ABC are in the ratio 2 : 7.
Let say 2x and 7x
DCB and ABC are adjacent angles
sum of adjacent angles in parallelogram = 180°
=> 2x + 7x = 180°
=> 9x = 180°
=> x = 20°
∠DCB = 2x = 2 * 20° = 40°
∠DCB = ∠DAB ( opposite angles of parallelogram )
=> ∠DAB = 40°
in Δ ABD
∠ADB + ∠ABD + ∠DAB = 180° ( sum of angles of triangle)
=> ∠ADB + ∠ABD + 40° = 180°
=> ∠ADB + ∠ABD = 140°
sum of ABD and ADB = 140°
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