Qstnid -C-12- The Following Figure Shows A Quadrilateral In Which Sides Ab And Dc Are Parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x - 15)° And ∠C = (4x + 20)°, Find Each Angle Of The Quadrilateral Abcd. <Img Border="0" Data-original-height="149" Data-original-width="247" Src="/etl/esadigi-best/content/system/stage/icse-viii-cmn/hwh-math-selina/c16/im019.png"> - 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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#12
The following figure shows a quadrilateral in which sides AB and DC are parallel. If ∠A : ∠D = 4 : 5, ∠B = (3x - 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.

Ans : Let ∠A = 4x
∠D = 5x
Since ∠A + ∠D = 180° [AB || DC]
4x + 5x = 180°
⇒ 9x = 180°
⇒ x = 20°
∠A = 4 (20) = 80°,
∠D = 5 (20) = 100°
Again ∠B + ∠C = 180° [ AB || DC]
3x - 15° + 4x + 20° = 180°
⇒ 7x = 180° - 5°
⇒ 7x = 175°
⇒ x = 25°
∠B = 75° - 15° = 60°
and ∠C = 4(25) + 20 = 100° + 20° = 120°