Question

Prove that the adjacent angles of a parallelogram are supplementary

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°. 

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

Answer:

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°.