Question

prove that the opposite angles of an isosceles trapezium 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 

Answer 2

Given: An isosceles Trapezium ABCD

To prove: Opposite angles are supplementary

Proof : AB||CD. Therefore, angle A + angle D =180°

Angle a = angle b (As the Trapezium is isosceles)

Angle b + angle d = 180°

Therefore, angle a + angle c = 180°

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