Mathematics

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


SOLUTION
Given $$ABCD$$ is isoscles trapezium in which $$AD=BC$$
To prove: $$(i)\angle A+\angle C=180$$
$$(ii)\angle B+\angle D=180^{o}$$
Proof:$$AB\parallel CD$$
$$\Rightarrow \angle A+\angle D=180$$
But $$\angle A=\angle B$$[Trapezium is isosceles]
$$\angle B+\angle D=180^{o}$$
Similarly $$\angle A+\angle C=180^{o}$$
Hence the result.
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