Are adjacent angles in a parallelogram supplementary?

Yes adjacent angles of a parallelogram are supplementary

Proof

Let us consider Parallelogram ABCD.

To prove: ∠A + ∠B = 180 degrees, ∠C + ∠D = 180 degrees

AB ∥ CD and AD is a transversal.

We know that interior angles on the same side of a transversal are supplementary.

Therefore, ∠A + ∠D = 180°

Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°.

Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.

Hence, it is proved that any two adjacent or consecutive angles of a parallelogram are supplementary.

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