Question

The angle of a triangle are 3x,(2x+20)°and (5x-40)°. Find the angle hence show that the triangle is an equilateral triangle

Answer 1

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A N S W E R :—

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• The angles measures 60°

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S O L U T I O N :—

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~Its given that the angle of a triangle are 3x, (2x + 20)° and (5x - 40)°. We have to find the angles and show that the triangle is an equilateral triangle. We also know that sum of an equilateral triangle is 180°.

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★ Using angle sum property :—

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$\tt→{3x + 2x + 20 + 5x - 40 = 180}$

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$\tt→{3x + 2x + 5x + 20 - 40 = 180}$

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$\tt→{10x + 20 - 40 = 180}$

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$\tt→{10x - 20 = 180}$

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$\tt→{10x = 180 + 20}$

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$\tt→{10x = 200}$

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$\tt→{x = \cancel \dfrac{200}{10} }$

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$\tt→{x = 20}$

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Therefore, the value of x is 60°.

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★ Substituting all the values :—

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$\tt→{3x = 3 \times 20 = 60} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \tt→{2x + 20 = 2 \times 20 + 20 = 40 + 20 = 60} \\ \\ \tt→{5x - 40 = 5 \times 20 - 40 = 100 - 40 = 60}$

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Therefore, all the angles of the triangle add up to 180° = equilateral triangle.

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