Question

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.

Answer 1

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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