Question

in an isosceles trapezium show that the opposite angles are supplementary

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 

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