Question

Prove that the adjacent angles of a parallelogram are supplementary.
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Answer 1

Step-by-step explanation:

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

Answer 2

Let ABCD be a parallelogram.Then AD∣∣BC & AB is transversal.

Therefore, A+B=1 same since, sum of the interior angles on the same since of the transversal is 180⁰)

Similarly, ∠B+∠C=180⁰ ,∠C+∠D=180⁰ & ∠D+∠A=180⁰

Thus, the sum of any 2 adjacent angles of a parallelogram is 180⁰ Hence any 2 adjacent angles of a parallelogram are supplementary.

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