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Question
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4 : 5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD
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Solution
(i) ∵ ∠A : ∠D = 1 : 2
Let ∠A = x and ∠D = 2x
∵ ∠C : ∠B = 4 : 5
Let ∠C = 4y and ∠B = 5y
∵ AB || DC
∴ ∠A + ∠D = 180°
x + 2x = 180°
3x = 180°
x = 60°
∴ A = 60°
∠D = 2x = 2 × 60 = 120°
Again ∠B + ∠C = 180°
5y + 4y = 180°
9y = 180°
y = 20°
∴ ∠B = 5y = 5 x 20 = 100°
∠C = 4y = 4 x 20 = 80°
Hence ∠A = 60°; ∠B = 100°; ∠C = 80°
and ∠D = 120°
(ii) `square` ABCD is a trapezium.
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