Question

Hindu figure ABCD is a parallelogram if angle dab kuchh 60 degree and angle DBC equal to 80 degree then find angle cdb.
pls help me ​

Answer 1

Question:-

In the figure ABCD is parallelogram. If Angle DAB = 60° and Angle DBC = 80°. Then find Angle CDB.

Answer:-

• Angle CDB is 40°

To find:-

• Angle CDB

Solution:-

• Angle DAB = 60°
• Angle DBC = 80°

We have to find angle DCB ,

$\large{ \tt : \implies \: \: \: \: \angle \: DAB = \angle \: DCB}$

• Because opposite angles of parallelogram are equal
• Then, Angle DCB = 60°

In the ️ triangle DBC,

• Sum of angles of triangle = 180°

According to question,

$\large{ \tt : \implies \: \: \: \angle \: DCB + \angle \: DBC + \angle \: CDB = 180 \degree}$

$\large{ \tt : \implies \: \: \: \: 60 \degree + 80 \degree + \angle CDB = 180 \degree}$

$\large{ \tt : \implies \: \: \: \: 140 \degree + \angle \: CDB = 180 \degree}$

$\large{ \tt : \implies \: \: \: \angle \: CDB = 180 \degree - 140 \degree}$

$\large{ \tt : \implies \: \: \: \angle CDB = 40 \degree}$

Hence,

Angle CDB is 40°

Answer 2

Given:

• ABCD is a parallelogram
• ∠ DAB = 80°
• ∠ DBC = 60°

To Find:

• ∠ CDB

Solution:

As we know,

• Opposite angles are equal in parallelogram

So we get

→∠ C = ∠ A = 80°

From the figure,

• AD || BC and BD is a transversal

We know that ∠ ADB and ∠ DBC are alternate angles,

So we get

∠ ADB = ∠ DBC = 60°

Consider △ ABD

Using the sum property of triangle

→ ∠ A + ∠ ADB + ∠ ABD = 180°

→ 80° + 60° + ∠ ABD = 180°

→ ∠ ABD = 180° – 80° – 60°

→ ∠ ABD = 180° – 140°

→ ∠ ABD = 40°

It can be written as

→∠ ABC = ∠ ABD + ∠ DBC

→ ∠ ABC = 40° + 60°

→ ∠ ABC = 100°

We know that the opposite angles are equal in a parallelogram

→ ∠ ADC = ∠ ABC = 100°

→ ∠ ADC = ∠ CDB + ∠ ADB

→ ∠ CDB = ∠ ADC – ∠ ADB

→ ∠ CDB = 100° – 60°

→ ∠ CDB = 40°

Therefore,

• ∠ ADB = 60° and ∠ CDB = 40°.