Show that the adjacent angles of a parallelogram are supplementary
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Prove that the adjacent angles of a parallelogram are supplementary
Answered by admin @
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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