Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Let ABCD be the parallelogram with ∠A = ∠B.

The sum of adjacent angles of a parallelogram is 180.

⇒  ∠A + ∠B = 180 

⇒  2∠A = 180 [∠A = ∠B ]

⇒  ∠A = 90 

⇒  ∠B = ∠A = 90 

⇒  ∠A = ∠C = 90 [Opposite angles of parallelogram]

⇒  ∠B = ∠D = 90 [Opposite angles of parallelogram]

∴  Each angle of the parallelogram measures is 90.

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