Ratio and Proportion – Maharashtra Board Class 9 Solutions for Algebra
AlgebraGeometryScience and TechnologyHindi
Exercise -6.1
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Let the common multiple be x.
∴ The measures of the angles are 2x°, 3x°, 4x° and x° respectively.
By the angle sum property of a quadrilateral,
2x° + 3x° + 4x° + x° = 360°
∴ 10x° = 360°
∴ x° = 36°
m∠D = x° = 36°
m∠A = 2x° = 2 × 36° = 72°
m∠B = 3x° = 3 × 36° = 108°
m∠C = 4x° = 4 × 36° = 144°
Now, m∠A + m∠B = 72° + 108° = 180° and
m∠C + m∠D = 144° + 36° = 180°
side AD ∥ side BC (By interior angle test for parallel lines.)
Again, m∠A + m∠D = 72° + 36° ≠ 180° and
m∠B + m∠C = 108° + 144° ≠ 180°
∴ Side AB is not parallel to side CD.
∴ Only one pair of opposite sides is parallel,
∴ □ABCD is a trapezium.
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Exercise – 6.2
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Exercise – 6.3
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Exercise – 6.4
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Exercise – 6.5
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