In the adjoining figure, ABCD is a trapezium in which AB || DC. If ∠A = 55° and ∠B = 70°, find ∠C and ∠D.

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Solution

We have AB || DC.
$∠$ A and $∠$ D are the interior angles on the same side of transversal line AD, whereas $∠$ B and $∠$ C are the interior angles on the same side of transversal line BC.
Now, $∠$ A + $∠$ D = 180^∘
⇒ $∠$ D = 180^∘ − $∠$ A
∴ $∠$ D = 180^∘ − 55^∘ = 125^∘

Again , $∠$ B + $∠$ C = 180^∘
⇒ $∠$ C = 180^∘− $∠$ B
∴ $∠$ C = 180^∘ − 70^∘ = 110^∘

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