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Question

# We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, ∠ABC= 110∘, ∠DAC = 15∘, ∠CAB= 25∘, AB = 5 cm, CD = 7 cm. Can we construct this parallelogram?

A

Yes, of course

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B

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C

With AC yes

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D

No, it is impossible

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Solution

## The correct option is D No, it is impossible 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∘ So, this construction is not possible.

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