**Ratio and Proportion – Maharashtra Board Class 9 Solutions for Algebra**

AlgebraGeometryScience and TechnologyHindi

**Exercise -6.1**

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**Solution 10:**

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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**Solution 11(iii):**

**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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