Question

In an Isosceles-trapezium, show that the opposite angles are supplementary.

Answer 1

Given : ABCD is isosceles trapezium in which AD = BC

To Prove : 
(i) ∠A + ∠C = 180°
(ii) ∠B + ∠D = 180°

Proof : AB || CD.

⇒ ∠A + ∠D = 180°

But ∠A = ∠B [Trapezium is isosceles)]

∠B + ∠D = 180°

Similarly ∠A + ∠C = 180°

Hence the result.