Question

2x 95 70° 1202 989 90° (v) (vi) (vii) (viii) 7. The angles of a triangle are in the ratio of 2:5: 8. Find the angles. 8. One angle of a triangle is 50º and the other two ar in the ratio 6 : 7. Find the anales.​

Answer 1

Given :

• The angles of a Triangle are in the ratio 2:5:8 .

To Find :

• Find the Angles

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

☆ We know That :

• Sum of Angles (Triangle) = 180°

☆ Let the Ratios :

• ∠1 = 2y
• ∠2 = 5y
• ∠3 = 8y

☆ Calculating the Value of y :

$➢ \qquad \;$ ∠1 + ∠2 + ∠3 = 180°

$\\ ➢ \qquad \;$ 2y + 5y + 8y = 180°

$\\ ➢ \qquad \;$ 7y + 8y = 180°

$\\ ➢ \qquad \;$ 15y = 180°

$\\ ➢ \qquad \;$ y = 180/15

• Cancelling 180 by 15 :

$\\ ➢ \qquad \; {\red{\pmb{\underline{\underline{\frak{ y = 12 }}}}}}$

☆ Calculating the Angles :

• ∠1 = 2y = 2(12) = 24°
• ∠2 = 5y = 5(12) = 60°
• ∠3 = 8y = 8(12) = 96°

☆ Therefore :

The three Angles are 24° , 60° and 96° .

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Answer 2

Given Information :-

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• The angles of a triangle are in ratio 2 : 5 : 8

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To Find :-

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• The value of angles

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Concept Used :-

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To solve this question, we will use the concept of angle sum property of a triangle is 180°. Using this concept, we get :-

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• ∠1 = 2x
• ∠2 = 5x
• ∠3 = 8x

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Now, using the same concept we will obtain an equation, that is :-

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$\sf \bigstar \:2x + 5x + 8x = 180^\circ$

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Now, we will equate it to get the required answer.

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Solution :-

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$\\ \sf \longrightarrow \: 2x + 5x + 8x = 180^\circ \\ \\ \\ \sf \longrightarrow \: 15x = 180^\circ \\ \\ \\ \sf \longrightarrow \: x = \frac{180^\circ}{15} \\ \\ \\ \sf \longrightarrow \: x = \cancel\frac{180^\circ}{15} = 12^\circ$

Now, we will put the value of x in their ratios and get the required answer.

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• ∠1 = 2x = 2 x 12 = 24°
• ∠2 = 5x = 5 x 12 = 60°
• ∠3 = 8x = 8 x 12 = 96°

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Verification :-

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For verification, we will add all the derived value and check if L.H.S. is equal to R.H.S.

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$\\ \sf\longrightarrow 24^\circ + 60^\circ + 96 ^\circ= 180^\circ \\ \\ \\ \sf\longrightarrow 120 ^\circ+ 60 ^\circ= 180^\circ \\ \\ \\ \sf\longrightarrow 180 ^\circ= 180^\circ \:$

Hence, verified.

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