The measure of an angle of a triangle are in the rotio 5:6:7, find the

1.	The measure of an angle of a triangle are in the rotio 5:6:7, find the measure
Answer» $\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$ $\:\:$ $\large\underline{\green{\bf Given :-}}$ $\:\:$ The measure of an angle of a triangle are in the ratio 5:6:7 $\:\:$ $\large\underline{\red{\bf To \: Find :-}}$ $\:\:$ The measure of angles $\:\:$ $\large\underline{\orange{\bf Solution :-}}$ $\:\:$ Let the 1st angle be 5x Let the 2nd angle be 6x Let the 3RD angle be 7x $\:\:$ $\purple{\underline \bold{According \: to \: the \ question :}}$ $\:\:$ The measure of an angle of a triangle are in the ratio 5:6:7 $\:\:$ $\underline{\bold{\texttt{1st angles :}}}$ $\:\:$ ➠ 5x ⚊⚊⚊⚊ ⓵ $\:\:$ $\underline{\bold{\texttt{2nd angle :}}}$ $\:\:$ ➠ 6x ⚊⚊⚊⚊ ⓶ $\:\:$ $\underline{\bold{\texttt{3rd angle :}}}$ $\:\:$ ➠ 7x ⚊⚊⚊⚊ ⓷ $\:\:$ Also we KNOW that sum of all angles of triangle is 180° $\:\:$ So, $\:\:$ ➜ 5x + 6x + 7x = 180 $\:\:$ ➜ 18X = 180 $\:\:$ ➜ $\sf x = \dfrac {180 } { 18 }$ $\:\:$ ➨ x = 10 $\:\:$ ⟮ Putting x = 10 in ⓵ ⟯ $\:\:$ ➜ 5x $\:\:$ ➜ 5(10) $\:\:$ ➨ 50 $\:\:$ Hence the 1st angle is 50° $\:\:$ ⟮ Putting x = 10 in ⓶ ⟯ $\:\:$ ➜ 6x $\:\:$ ➜ 6(10) $\:\:$ ➨ 60 $\:\:$ Hence 2nd angle is 60° $\:\:$ ⟮ Putting x = 10 in ⓷ ⟯ $\:\:$ ➜ 7x $\:\:$ ➜ 7(10) $\:\:$ ➨ 70° $\:\:$ Hence 3rd angle is 70° $\:\:$ ∴ The angles are 50° , 60° , 70° $\:\:$ ━━━━━━━━━━━━━━━━━━━━━━━━━ Verification $\:\:$ Sum of all angles of a triangle is 180° $\:\:$ 50° + 60° + 70° = 180° $\:\:$ *Verified* ═════════════════════════

The measure of an angle of a triangle are in the rotio 5:6:7, find the measure

Answer»

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large\underline{\green{\bf Given :-}}$

$\:\:$

The measure of an angle of a triangle are in the ratio 5:6:7

$\:\:$

$\large\underline{\red{\bf To \: Find :-}}$

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The measure of angles

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$\large\underline{\orange{\bf Solution :-}}$

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Let the 1st angle be 5x

Let the 2nd angle be 6x

Let the 3RD angle be 7x

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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The measure of an angle of a triangle are in the ratio 5:6:7

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

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➠ 5x ⚊⚊⚊⚊ ⓵

$\:\:$

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

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➠ 6x ⚊⚊⚊⚊ ⓶

$\:\:$

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

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➠ 7x ⚊⚊⚊⚊ ⓷

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Also we KNOW that sum of all angles of triangle is 180°

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So,

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➜ 5x + 6x + 7x = 180

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➜ 18X = 180

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➜ $\sf x = \dfrac {180 } { 18 }$

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➨ x = 10

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⟮ Putting x = 10 in ⓵ ⟯

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➜ 5x

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➜ 5(10)

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➨ 50

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Hence the 1st angle is 50°

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⟮ Putting x = 10 in ⓶ ⟯

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➜ 6x

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➜ 6(10)

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➨ 60

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Hence 2nd angle is 60°

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⟮ Putting x = 10 in ⓷ ⟯

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➜ 7x

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➜ 7(10)

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➨ 70°

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Hence 3rd angle is 70°

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∴ The angles are 50° , 60° , 70°

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━━━━━━━━━━━━━━━━━━━━━━━━━

Verification

$\:\:$

Sum of all angles of a triangle is 180°

$\:\:$

50° + 60° + 70° = 180°

$\:\:$

Verified

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