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Question
ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.
Solution
Given, ABCD is a trapezium and whose parallel sides in the figure are AB and DC.
Since, AB || CD and BC is transversal, then sum of two cointerior angles is 180°.
∴ ∠B + ∠C = 180º
⇒ ∠C = 180º – ∠B = 180º – 45º ...[∵ ∠B = 45º given]
⇒ ∠C = 135º
Similarly, ∠A + ∠D = 180º ...[Sum of cointerior angles is 180º]
⇒ ∠D = 180º – 45º ...[∵ ∠A = 45º given]
⇒ ∠D = 135º
Hence, angles C and D are 135º each.
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