Question

The angles of a triangle are in the ratio 5 : 3 : 7 then anwer the following
2 . here the measure of greatest angle is

90 degree
36 degree
84 degree
86 degree



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Answer 1

We've to find out the Greatest angles of the given triangle. First We'll find all three angles of the triangle. & to find angles we'll use Angle sum property of triangle i.e (∠A + ∠B + ∠C = 180°).

So Let's Consider the angles of a triangle be 5x, 3x and 7x respectively.

⠀

$\bf{\dag}\;{\underline{\frak{As\;we\;know\;that,}}}$

• Sum of all angles of a triangle is 180°.

⠀

$:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ$

$\sf Here \begin{cases} & \sf{\angle\:A = \bf{5x}} \\ & \sf{\angle\:B = \bf{3x}} \\ &\sf{\angle\:C = \bf{7x}}\end{cases}$

$\bf{\dag}\;{\underline{\frak{ Substituting\:values,}}}$

$:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ\\\\\\:\implies\sf 5x + 3x + 7x = 180^{\circ}\\\\\\:\implies\sf 15x = 180^\circ\\\\\\:\implies\sf x = \cancel\dfrac{180^\circ}{15}\\\\\\:\implies\underline{\boxed{\pmb{\frak{\pink{x = 12}}}}}\;\bigstar$

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Therefore, Angles of ∆ are :

⠀

• 5x = 5(12) = 60°
• 3x = 3(12) = 36°
• 7x = 7(12) = 84°

⠀

$\therefore\:{\underline{\sf{Measure\: of\; Greatest\: angle\:of\:a\:\triangle\:is\:{\sf{\pmb{Option\;c)\;84^\circ}.}}}}}$

Answer 2

Answer:

Given :-

• The angles of a triangle are in the ratio of 5 : 3 : 7.

To Find :-

• What is the greatest angles of a triangle.

Solution :-

Let,

$\mapsto \bf First\: Angle_{(Triangle)} =\: 5a$

$\mapsto \bf Second\: Angle_{(Triangle)} =\: 3a$

$\mapsto \bf Third\: Angle_{(Triangle)} =\: 7a$

As we know that :

$\footnotesize\bigstar \: \: \sf\boxed{\bold{\pink{Sum\: Of\: All\: Angles\: Of\: Triangle =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\footnotesize \implies \bf First\: Angle + Second\: Angle + Third\: Angle =\: 180^{\circ}$

$\implies \sf 5a + 3a + 7a =\: 180^{\circ}$

$\implies \sf 8a + 7a =\: 180^{\circ}$

$\implies \sf 15a =\: 180^{\circ}$

$\implies \sf a =\: \dfrac{\cancel{180^{\circ}}}{\cancel{15}}$

$\implies \sf a =\: \dfrac{12^{\circ}}{1}$

$\implies \sf\bold{\purple{a =\: 12^{\circ}}}$

Hence, the required measure of angles of a triangle are :

❒ First Angle Of Triangle :

$\longrightarrow \sf First\: Angle_{(Triangle)} =\: 5a$

$\longrightarrow \sf First\: Angle_{(Triangle)} =\: 5 \times 12^{\circ}$

$\longrightarrow \sf\bold{\red{First\: Angle_{(Triangle)} =\: 60^{\circ}}}$

❒ Second Angle Of Triangle :

$\longrightarrow \sf Second\: Angle_{(Triangle)} =\: 3a$

$\longrightarrow \sf Second\: Angle_{(Triangle)} =\: 3 \times 12^{\circ}$

$\longrightarrow \sf\bold{\red{Second\: Angle_{(Triangle)} =\: 36^{\circ}}}$

❒ Third Angle Of Triangle :

$\longrightarrow \sf Third\: Angle_{(Triangle)} =\: 7a$

$\longrightarrow \sf Third\: Angle_{(Triangle)} =\: 7 \times 12^{\circ}$

$\longrightarrow \sf\bold{\red{Third\: Angle_{(Triangle)} =\: 84^{\circ}}}$

${\small{\bold{\underline{\therefore\: The\: greatest\: angles\: of\: a\: triangle\: is\: 84^{\circ}\: .}}}}$

Hence, the correct options is option no (c) 84°.

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★ VERIFICATION ★

As we know that :

$\footnotesize\clubsuit\: \: \sf\boxed{\bold{\pink{Sum\: Of\: All\: Angles\: Of\: Triangle =\: 180^{\circ}}}}\: \: \clubsuit$

$\leadsto \sf 5a + 3a + 7a =\: 180^{\circ}$

By putting a = 12° we get,

$\leadsto \sf 5(12^{\circ}) + 3(12^{\circ}) + 7(12^{\circ}) =\: 180^{\circ}$

$\leadsto \sf 60^{\circ} + 36^{\circ} + 84^{\circ} =\: 180^{\circ}$

$\leadsto \sf\bold{\green{180^{\circ} =\: 180^{\circ}}}$

Hence, Verified.