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प्रश्न
The angles A, B, C and D of a trapezium ABCD are in the ratio 3: 4: 5: 6. Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer.
उत्तर
As the trapezium ABCD is a quadrilateral,
∴ Sum of its interior angles = 360°
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ 3x + 4x + 5x + 6x = 360°
⇒ 18x = 360°
⇒ x = `360^circ/18 = 20°`
∴ ∠A = 3x = 3 × 20° = 60°
and ∠B = 4x = 4 × 20° = 80°
and ∠C = 5x = 5 × 20° = 100°
and ∠D = 6x = 6 × 20° = 120°
AB is parallel to DC.
∵ ∠A + ∠D = 180°
∠A and ∠D are co-interior angles whose sum = 180°
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