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सी.आई.एस.सी.ई.आईसीएसई ICSE Class 8

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. - Mathematics

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प्रश्न

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.

योग
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उत्तर

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°

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अध्याय 27: Quadrilateral - Exercise 27 (A)

APPEARS IN

सेलिना Mathematics [English] Class 6
अध्याय 27 Quadrilateral
Exercise 27 (A) | Q 12
सेलिना Concise Mathematics [English] Class 8 ICSE
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Exercise 16 (C) | Q 12 | पृष्ठ १८७

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