Prove that adjacent angles of a parallelogram are supplementary

Asked by admin @ 20/08/2021 in Math viewed by 395 People

Prove that the adjacent angles of a parallelogram are supplementary

Answered by admin @ 20/08/2021

Let ABCD be a parallelogram

Then, AD ∥ BC and AB is a transversal.

Therefore, A + B = 180° [Since, sum of the interior angles on the same side of the transversal is 180°]

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

Thus, the sum of any two adjacent angles of a parallelogram is 180°.

Hence, any two adjacent angles of a parallelogram are supplementary.

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