Are adjacent angles in a parallelogram supplementary?

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Solution

Yes adjacent angles of a parallelogram are supplementary
Proof,
Let us consider Parallelogram $A B C D$ .
To prove: $∠ A + ∠ B = 180 °, ∠ C + ∠ D = 180 °$
We have, $A B ∥ C D$ and $A D$ is a transversal.
We know that interior angles on the same side of a transversal are supplementary.
Therefore, $∠ A + ∠ D = 180 °$
Similarly, $∠ B + ∠ C = 180 °, ∠ C + ∠ D = 180 °, ∠ A + ∠ B = 180 ° .$
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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