Question

Prove that opposite angles of an iscoceles trapezium are supplementry

Answer 1

In an isosceles trapezium AB is parallel to DC and the alternate interior angles are supplementary. So, the angles ∠A and ∠D are supplementary.which means
∠A + ∠D = 180

Similarly, ∠B and ∠C are supplementary.
so, ∠B + ∠C = 180
Since the trapezium is the isosceles trapezium, the base angles are equal. ∠C = ∠DSo by subsituting the anles we get
∠A + ∠C = 180
∠B + ∠D = 180

so the opposite angles are also supplementary