Question

in a quadrilateral ABCD, AB || CD, angle A: angleD =4:5, angle B= (3x - 15) °and 2C = (4x + 20)°. Find each and of the quadrilateral ABCD.​

Answer 1

Answer:

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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