Qstnid -C-5- 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 - 16: Understanding Shapes (Including Polygons) Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

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#5
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
Ans :
∵ ∠A : ∠D = 1 : 2
Let ∠A = x and ∠B = 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 × 20˚ = 100˚
∠C = 4y = 4 × 20˚ = 80˚
Hence ∠A = 60˚ : ∠B = 100˚ : ∠C = 80˚ ∠D = 120˚
(iii) Quadrilateral ABCD is a trapezium because one pair of opposite side is parallel.