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Question

Are adjacent angles in a parallelogram supplementary?


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Solution

Yes adjacent angles of a parallelogram are supplementary

Proof,

Let us consider ParallelogramABCD.

To prove: A+B=180°,C+D=180°

We have, ABCD andAD 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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