Question

Prove that any two adjacent angles of a parallelogram are supplementary. [2 Marks]

Answer 1

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°. [1 Mark]

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

Hence, any two adjacent angles of a parallelogram are supplementary. [1 Mark]