Question

Prove that the opposite angles of a parallelogram are equal.

Answer 1

Let ABCD be the given parallelogram. So, AD||BC and AB||DC.

Let ∠A = x

Then ∠D = ${180}^{\circ }$ - ∠A = ${180}^{\circ }$ - x (Because ∠A and ∠D are interior opposite angles)

∠C = ${180}^{\circ }$ - ∠D = x

∠B = ${180}^{\circ }$ - ∠A = ${180}^{\circ }$ - x

Thus, we can see that the opposite angles A and C are equal; and the opposite angles B and D are also equal.