Question

Angles of a triangle are in the
ratio 2:3:4,the smallest angle of thetriangle is​

Answer 1

Answer:

18°

Step-by-step explanation:

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Answer 2

GivEn:

• Angles of a triangle are in the ratio 2:3:4.

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To find:

• Smallest angle of triangle.

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SoluTion:

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${\underline{\sf{\bigstar\;As\;per\;given\; Question\;:}}}$

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Angles of a triangle are in the ratio 2:3:4.

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☯ Let angles of triangle in term of x i.e. 2x, 3x and 4x.

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As we know that,

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Sum of all angles of a triangle is 180°. (Angle sum property)

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$:\implies\sf 2x + 3x + 4x = 180^\circ$

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$:\implies\sf 9x = 180^\circ$

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$:\implies\sf x = \cancel{ \dfrac{180^\circ}{9}}$

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$:\implies{\underline{\boxed{\bf{\pink{x = 20^\circ}}}}}\;\bigstar$

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Therefore,

Angles of Triangle are,

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• First angle, 2x = 2 × 20 = 40°
• Second angle, 3x = 3 × 20 = 60°
• Third angle, 4x = 4 × 20 = 80°

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As we can see that, 40° is the smallest of all.

$\therefore$ 40° is the smallest angle of given triangle.