Question

which is in the shape of a parallelogram (see the adjoining figure) whose two adjacent angles are in the ratio 2:3 Find the  measure of angle A​

Answer 1

Answer:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180

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⇒3x+2x=180

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⇒5x=180

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⇒x=

5

180

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=36

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∴∠3×36

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=108

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and, ∠B=2×36

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=72

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Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108

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and ∠D=∠B=72

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Hence, ∠A=108

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,∠B=72

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,∠C=108

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and ∠D=72

o