Question
We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, ∠ ABC = 110∘, ∠ DAC = 15∘, ∠ CAB=25∘, AB = 5cm, CD = 7cm. Can we construct this parallelogram?
Answer: Option D
:
D
Step1: Draw rough diagram of the parallelogram ABCD
Here, ∠DAC = ∠ ACB= 15∘ - (1) (Alternate interior angles)
In △ABC,
∠ A + ∠ B + ∠ C must be 180∘
∠ A + ∠ B + ∠ C = 25∘ + 110∘ + 15∘ (from (1))
∠ A + ∠ B + ∠ C = 150∘
The sum of angles in a triangle should always be equal to 180∘. So, this construction is not possible.
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:
D
Step1: Draw rough diagram of the parallelogram ABCD
Here, ∠DAC = ∠ ACB= 15∘ - (1) (Alternate interior angles)
In △ABC,
∠ A + ∠ B + ∠ C must be 180∘
∠ A + ∠ B + ∠ C = 25∘ + 110∘ + 15∘ (from (1))
∠ A + ∠ B + ∠ C = 150∘
The sum of angles in a triangle should always be equal to 180∘. So, this construction is not possible.
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