Qstnid -C-10- In Quadrilateral Pqrs, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7. Calculate Each Angle Of The Quadrilateral And Then Prove That Pq And Sr Are Parallel To Each Other (I) Is Ps Also Parallel To Qr? (Ii) Assign A Special Name To Quadrilateral Pqrs. - 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

with Solutions - page 8

Qstn# C-10 Prvs-Qstn Next-Qstn

#10
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other (i) Is PS also parallel to QR? (ii) Assign a special name to quadrilateral PQRS.
Ans : ∵ ∠P : ∠Q + ∠R : ∠S = 3 : 4 : 5 : 6
Let ∠P = 3x
∠Q = 4x
∠R = 6x
∠S = 7x
∴ ∠P + ∠Q + ∠R + ∠S = 360˚
⇒ 3x + 4x + 6x + 7x = 360˚
⇒ 20x = 360˚
⇒ x = 18˚
∴ ∠P = 3x = 3 × 18 = 54˚
∠Q = 4x = 4 × 18 = 72˚
∠R = 6x = 6 × 18 = 108˚
∠S = 7x = 7 × 18 = 126˚
∠Q + ∠R = 72˚ + 108˚ = 180˚
Or ∠P + ∠S = 54˚ + 126 ˚ = 180˚
Hence PQ ∥ SR
As ∠P + ∠Q = 72˚ + 54˚ = 126˚
Which is ≠ 180˚
∴ PS and QR are not parallel.
(ii) PQRS is a trapezium as its one pair of opposite side is parallel.