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In the adjoining figure, ABCD is a parallelogram in which $∠ A$ =72°. The measure of ∠B, $∠ C, ∠ D$ are:

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∠ B = 150 °, ∠ C = 72 ° and ∠ D = 18 °

∠ B = 18 °, ∠ C = 56 ° and ∠ D = 108 °

∠ B = 108 °, ∠ C = 72 ° and ∠ D = 108 °

∠ B = 108 °, ∠ C = 72 ° and ∠ D = 99 °

answer is C.

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Detailed Solution

Given a parallelogram ABCD having

∠ A

=72°.

In the adjoining figure, ABCD is a parallelogram in which ∠ A = 72∘. Calculate ∠ B, ∠ C and ∠ D.

Since, opposite angles of a parallelogram are equal.

⇒ ∠ A = ∠ C = 72 ° ⇒ ∠ B = ∠ D

Now, as sum of all the angles of a quadrilateral =

360 °

∠ A + ∠ B + ∠ C + ∠ D = 360 ° 72 ° + ∠ B + 72 ° + ∠ B = 360 ° 2 × ∠ B = 360 ° − 144 ° ∠ B = 108 °

The measure of angles is

∠ B = 108 °, ∠ C = 72 ° and ∠ D = 108 °

.
Hence, option 3 is correct.

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