Question

The angles of a triangle are in the ratio 2:3:4 find the angles

Answer 1

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

Given thαt,

• The αngles of α triαngle αre in the rαtio 2:3:4.

◾️We hαve to find the αctuαl vαlue of αngles.

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To do so,

Let's αssume the αngles to be 2x, 3x αnd 4x.

$\large\star{\boxed{\sf{\purple{ Angle\:Sum\:Property_{(triangle)} = 180^{\circ}}}}}$

According to the question,

$\longrightarrow{\sf{ 2x + 3x + 4x= 180^{\circ}}}$

$\longrightarrow{\sf{9x= 180^{\circ}}}$

$\longrightarrow{\sf{x= \dfrac{180^{\circ}}{9}}}$

$\longrightarrow{\sf{x= 20^{\circ}}}$

Therefore, the αngles αre —

$\longrightarrow{\sf{ 2x = {\purple{40^{\circ}}}}}$

$\longrightarrow{\sf{ 3x = {\purple{60^{\circ}}}}}$

$\longrightarrow{\sf{ 4x ={\purple{80^{\circ}}}}}$

And we αre done! :D

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Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The angles of a triangle are in the ratio 2:3:4 find the angles

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• All angles

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We are given that the angles of triangle are in ratio 2:3:4

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So,

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• Let the 1st angle be 2a

• Let the 2nd angle be 3a

• Let the 3rd angle be 4a

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By angle sum property of triangle we came to know that the sum of all three angles of triangle is 180°

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i.e

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1st Angle + 2nd Angle + 3rd Angle = 180° ⚊⚊ ⓵

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$\underline{\bold{\texttt{For the given triangle :}}}$

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• 1st Angle = 2a ⚊⚊⚊⚊ ⓶

• 2nd Angle = 3a ⚊⚊⚊⚊ ⓷

• 3rd Angle = 4a ⚊⚊⚊⚊ ⓸

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⟮ Putting all angles in ⓵ ⟯

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➜ 1st Angle + 2nd Angle + 3rd Angle = 180°

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➜ 2a + 3a + 4a = 180°

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➜ 9a = 180

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➜ $\sf a = \dfrac { 180 } { 9 }$

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➜ a = 20 ⚊⚊⚊⚊ ⓹

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⟮ Putting a = 20 from ⓹ to ⓶ ⟯

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$\underline{\bold{\texttt{1st Angle :}}}$

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➜ 2a

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➜ 2(20)

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➨ 40°

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• Hence the 1st angle is 40°

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⟮ Putting a = 20 from ⓹ to ⓷ ⟯

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$\underline{\bold{\texttt{2nd Angle :}}}$

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➜ 3a

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➜ 3(20)

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➨ 60°

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• Hence the 2nd angle is 60°

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⟮ Putting a = 20 from ⓹ to ⓸ ⟯

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$\underline{\bold{\texttt{3rd Angle :}}}$

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➜ 4a

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➜ 4(20)

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➨ 80°

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• Hence the 3rd angle is 80°

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∴ The angles of triangle are 40° , 60° & 80°