Question

if the angles of
triangle are
(3x-5), (2x -15) and (5x-50), then
the values of
least angles and greatest angles are
​

Answer 1

A n s w e r

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G i v e n

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• Angles of triangle are (3x - 5), (2x - 15) & (5x - 50)

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F i n d

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• Least angle

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• Greatest angle

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S o l u t i o n

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We know that the sum of interior angles of triangle is 180°

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So ,

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Angle 1 + Angle 2 + Angle 3 = 180° ⚊⚊⚊⚊ ⓵

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• Angle 1 = (3x - 5) ⚊⚊⚊⚊ ⓶

• Angle 2 = (2x - 15) ⚊⚊⚊⚊ ⓷

• Angle 3 = (5x - 50) ⚊⚊⚊⚊ ⓸

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⟮ Putting the above values in ⓵ ⟯

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Angle 1 + Angle 2 + Angle 3 = 180°

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➜ 3x - 5 + 2x - 15 + 5x - 50 = 180

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➜ 10x - 70 = 180

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➜ 10x = 180 + 70

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➜ 10x = 250

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➨ x = 25° ⚊⚊⚊⚊ ⓹

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⟮ Putting x = 25 from ⓹ to ⓶ ⟯

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➜ Angle 1 = (3x - 5)

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➜ Angle 1 = (3(25) - 5)

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➨ Angle 1 = 70° ⚊⚊⚊⚊ ⓺

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• Hence Angle 1 is 70°

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⟮ Putting x = 25 from ⓹ to ⓷ ⟯

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➜ Angle 2 = (2x - 15)

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➜ Angle 2 = (2(25) - 15)

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➨ Angle 2 = 35° ⚊⚊⚊⚊ ⓻

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• Hence Angle 2 is 35°

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⟮ Putting x = 25 from ⓹ to ⓸ ⟯

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➜ Angle 3 = (5x - 50)

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➜ Angle 3 = (5(25) - 50)

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➨ Angle 3 = 75° ⚊⚊⚊⚊ ⓼

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• Hence Angle 3 is 75°

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From ⓺ , ⓻ & ⓼ we got that the least angle is Angle 2 i.e (2x - 15)

and the greatest angle is Angle 3 i.e (5x - 50)