Question

In the adjoining figure, ABCD is a parallelogram. If angle DAB =85°and angle DBC =60° ,then calculate :
(i) angle CDB (ii) angle ABD​

Answer 1

Given:-

• ABCD is parallelogram.
• ∠DAB = 85°.
• ∠DBC = 60°.

To find:-

1. ∠CDB
2. ∠ABC

Solution:-

Let ∠CDB be ∠1

And ∠ABD be ∠2.

_______________________________

• We know that , opposite angles of parallelogram are equal. So,

∠C = ∠DAB = 85° -------(i)

• We also know that, Sum of all interior angles of parallelogram are equal to 180°. This statement is also known as 'Angle sum property of triangle'.

So,

⇒∠1 + ∠C + ∠DBC = 180°.

• ∠DBC = 60° [Given]
• ∠C = 85° [By equation (i)]

⇒∠1 + 85° + 60° = 180°

⇒∠1 + 145° = 180°

⇒∠1 = 180° - 145°

⇒∠1 = 35°

We have taken ∠1 to be ∠CDB.

Therefore,

∠CDB is 35°

____________________________

• We know that, Sum of two adjacent angles of parallelogram is equal to 180°.

So,

⇒∠DAB + ∠2 + ∠DBC = 180°

• ∠DAB = 85° [Given]
• ∠DBC = 60° [Given]

⇒85° + ∠2 + 60° = 180°

⇒∠2 + 145° = 180°

⇒∠2 = 180° - 145°

⇒∠2 = 35°

We have taken ∠2 be ∠ABD

Therefore,

∠ABD is 35°.