Question

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

Answer 1

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

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

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

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

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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

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

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➠ 6x ⚊⚊⚊⚊ ⓶

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

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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

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Sum of all angles of a triangle is 180°

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50° + 60° + 70° = 180°

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Verified

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Answer 2

Given : The angles of Triangle are in ratio 5:6:7.

To find : Measure of each angle

Solution : Let the first angle = 5x

ㅤㅤLet the second angle = 6x

ㅤㅤLet the third angle = 7x

ㅤㅤ

We know, The sum of angles of triangle = 180°

ㅤㅤ•°• , 5x + 6x + 7x = 180°

ㅤㅤ

ㅤㅤㅤㅤ18x = 180°

ㅤㅤㅤㅤ

ㅤㅤㅤㅤx = 180/18

ㅤㅤㅤㅤ

ㅤㅤㅤㅤx = 10°

Therefore, first angle = 5x = 5(10)= 50°

ㅤㅤㅤㅤSecond angle = 6x = 6(10) = 60°

ㅤㅤㅤㅤThird angle = 7x = 7(10) = 70°