Question

In the adjoining figure, ABCD is a parallelogram in which ∠ DAB = 80° and ∠ DBC = 60°. Calculate ∠CDB and ∠ ADB.

Answer 1

It is given that ABCD is a parallelogram in which ∠ DAB = 80^o and ∠ DBC = 60^o

We know that opposite angles are equal in parallelogram

So we get

∠ C = ∠ A = 80^o

From the figure we know that AD || BC and BD is a transversal

We know that ∠ ADB and ∠ DBC are alternate angles

So we get

∠ ADB = ∠ DBC = 60^o

Consider △ ABD

Using the sum property of triangle

∠ A + ∠ ADB + ∠ ABD = 180^o

By substituting values in the above equation

80^o + 60^o + ∠ ABD = 180^o

On further calculation

∠ ABD = 180^o – 80^o – 60^o

By subtraction

∠ ABD = 180^o – 140^o

So we get

∠ ABD = 40^o

It can be written as

∠ ABC = ∠ ABD + ∠ DBC

By substituting values we get

∠ ABC = 40^o + 60^o

By addition

∠ ABC = 100^o

We know that the opposite angles are equal in a parallelogram

∠ ADC = ∠ ABC = 100^o

We get

∠ ADC = ∠ CDB + ∠ ADB

On further calculation

∠ CDB = ∠ ADC – ∠ ADB

By substituting values

∠ CDB = 100^o – 60^o

By subtraction

∠ CDB = 40^o

Therefore, ∠ ADB = 60^o and ∠ CDB = 40^o.