Question

In Fig. below, ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Compute

∠CDB and ∠ADB.

Answer 1

To find `∠`CDB and `∠`ADB

`∠`CBD = `∠`ABD = 60°     [Alternative interior angle AD || BC and BD is the transversal]

In a  parallelogram ABCD 

`∠`A = `∠`C = 75°                                [  ∵ Opposite side angles of a parallelogram are equal]

In `∠`BDC

`∠`CBD + `∠`C + `∠`CDB =180°                                                  [Angle sum property]

⇒ 60° + 75° + `∠`CDB = 180°

⇒`∠`CDB = 180° - (60° + 75°)

⇒ `∠`CDB = 45°

Hence `∠`CDB = 45°, `∠`ADB = 60°