Question

In Quadrilateral ABCD, side AB is parallel to side DC. ∠A: ∠D= 1:2 and ∠C:∠B= 4:5.
i) calculate each angle of the quadrilateral
ii) assign a special name to this quadrilateral

Answer 1

Answer:

Angle A=30, B =60 ,c =120 D=150.. trapezium

Answer 2

Given : ∠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° and ∠D = 120°

(ii) Quadrilateral ABCD is a trapezium because one pair of opposite side is parallel.

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