Question

Ln the parallelogram ABCD , angle BAD=75 and angle CBD=60 then the value of angle BDC =?

Answer 1

Answer-

In Parallelogram ABCD,

∠BAD = ∠BCD = 75° [Opposite angles of a parallelogram are equal]

In ΔBCD, By angle sum property

 

∠BCD + ∠BDC + ∠CBD = 180°

 

⇒ 75°+ ∠BDC + 60° = 180°

 

⇒ ∠BDC = 45°

Answer 2

∠BDC = 150°

Consider a parallelogram ABCD  with four vertices A, B, C, D and four angles ∠DAB, ∠CBA, ∠DCB, ∠ADC.

Now, Given that,

∠BAD = 75° and ∠CBA = 60°.

Now, the properties of a parallelogram are:

• Opposite angles are equal
• Opposite sides are equal and parallel
• Diagonals bisect each other
• Sum of any two adjacent angles is 180°

Thus, ∠BAD = ∠BCD = 75°.

And we know in a quadrilateral, the sum of all interior angles is 360°.

∴ ∠DAB+∠CBA+∠DCB+∠ADC = 360°

∴ 75° + 60° + 75° + ∠ADC = 360°

∴ ∠ADC = 150°