Question

In Fig. 14.35, ABCD is a parallelogram in which ∠DAB =75° and ∠DBC = 60°. Compute ∠CDB and ∠ADB.

Answer 1

∠CDB= 45° and ∠ADB=60°  

Step-by-step explanation:

• Given data

       ∠DAB =75°

       ∠DBC = 60°

• Here ABCD is a parallelogram

        Where AD =BC  and also AD║BC

        AB =CD  and also AB║CD

• ∠ADB = ∠DBC  (alternate interior angle)

       ∠ADB =  60°         Answer

• ∠BCD =∠DAB    (Opposite angle are equal in parallelogram)

       ∠BCD =75°

• Now consider triangle ΔBCD and use triangle angle property

       ∠CDB + ∠DBC +∠BCD = 180°

       ∠CDB+ 60° +75° = 180°

       ∠CDB = 180° - 60° -75°

       ∠CDB = 180° - 60° -75°

      ∠CDB = 45°         Answer

Answer 2

Figure:-

Given:-

• ABCD is a parallelogram.
• ∠DAB =75° and ∠DBC = 60°.

To find:-

• Find the ∠CDB and ∠ADB...?

Solutions:-

• ABCD is a parallelogram.

Thus, AD //BC

<DBC are <ADB alternate interior opposite angles.

Therefore,

=> <ADB = <DBC

=> <ADB = 60° ......(i).

We know that,

The opposite angles of a parallelogram are equal.

Therefore,

=> <A = <C

Also, we have <A = 75°

Therefore,

=> <C = 75° .......(ii).

In ∆BCD

By angle sum property of a triangle.

=> <CDB + <ADB + <C = 180°

From (i). and (ii). we get;

=> <CDB + 60° + 75° = 180°

=> <CDB + 135° = 180°

=> <CDB = 180° - 135°

= <CDB = 45°

Hence, the required value of <ADB is 60° and <CDB is 45°.