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