Mathematics
In the given figure, ABCD is an isosceles trapezium in which ∠CDA = 2x° and ∠BAD = 3x°. Find all the angles of the trapezium.
Rectilinear Figures
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Answer
We know that,
Sum of adjacent co-interior angles of a trapezium = 180°
∴ ∠A + ∠D = 180°
⇒ 3x + 2x = 180°
⇒ 5x = 180°
⇒ x =
⇒ x = 36°.
∠A = 3x = 3(36°) = 108°
∠D = 2x = 2(36°) = 72°
∠B = ∠A = 108° [∵ base angles of an isosceles trapezium are equal]
∠C = ∠D = 72° [∵ base angles of an isosceles trapezium are equal]
Hence, ∠A = 108°, ∠C = 72°, ∠B = 108° and ∠D = 72°.
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