Question

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

Answer 1

A triangle is said to be equilateral, if all the sides or all the angles are equal.

Since all angles are equal, the given triangle is an equilateral triangle.

Hope it helps u........mark as brainliest.

Answer 2

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A N S W E R :—

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• The angles are 60°.

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S O L U T I O N :—

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~Its given that the angles of a triangle are 3x° , (2x + 20)° and (5x - 40)°. We have to show that the triangle is an equilateral triangle. We also know that the 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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$\begin{gathered}{ \underline{ \red{ \boxed{ \sf{Therefore, \: the \: value \: of \: x \: is \: 20}}}}} \end{gathered}$

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★ Substituting all the values :—

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$\tt→{3x = 3 \times 20 = 60}$

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$\tt→{2x + 20 = 2 \times 20 + 20 = 40 + 20 = 60}$

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$\tt→{5 \times - 40 = 5 \times 20 - 40 = 100 - 40 = 60}$

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$\begin{gathered}{ \underline{ \red{ \boxed{ \sf{Therefore, \: the \: three \: angles \: add \: up \: to \: 180 = equileteral \: triangle}}}}} \end{gathered}$

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Hence, solved.

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