Question

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

Answer 1

Given: ABCD is isosceles trapezium in which AD = BC

$\text{To Prove: (i)}\angle A+\angle C=180$

$\text{(ii)}\angle B+\angle D={180}^{\circ }$

Proof: AB ‖ CD

$\Rightarrow \angle A+\angle D=180$

$\text{But}\angle A=\angle B\text{[Trapezium is isosceles)]}$

$\angle B+\angle D={180}^{\circ }$

$\text{Similarly}\angle A+\angle C={180}^{\circ }$

Hence the result.