Question

The angles of a triangle are in the ratio 3:5:7.
Find the measure of each angle of thetriangle.

(Hint: We know that the sum of the angles of a triangle is 180°.]
​

Answer 1

Answer:

36°,60°,84°

Step-by-step explanation:

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Answer 2

Correct Question-:

• The angles of a triangle are in the ratio 3:5:7. Find the measure of each angle of the triangle.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ The\:measure \:of\:the\:angles \:of\:triangles\:is\:36^{⁰},\:60^{⁰}\:and\:84^{⁰}}}}}}$

$\dag{\underline {\sf{\large { Explanation \: -: }}}}$

• $\frak{Given \:\: -:} \begin{cases} \sf{ The \:angles\: of \:a \:triangle\: are\: in \:the\: ratio\: 3:5:7\:. }\end{cases}$

• $\frak{To \:Find\: -:} \begin{cases} \sf{ The\:measure \:of\:three\:angles\: of \:a \:triangle\: . }\end{cases}$

$\dag{\underline {\sf{\large { As\:we\:know\:that\: -: }}}}$

$\frak{Let's \:Assume \: -:} \begin{cases} \sf{The\:measure\:of\:three \:angles\:of\:Triangle \:\:be\:= \frak{3x\:,5x\:and\;7x}} \end{cases}$

$\star {\bigstar {\sf{\large { Then\: -: }}}}$

• $\frak{Measure \:of\:Angles\: -:} \begin{cases} \sf{Angle_{1}= 3x}& \\\\ \sf{Angle _{2}= 5x}& \\\\ \sf{ Angle _{3}=7x}\end{cases}$

• $\underline{\boxed{\star{\sf{\blue{ The\:sum\:of\:the\:angles \:of\:triangles\:is\:180^{⁰}}}}}}$

• $\sf{Or,}$

• $\underline{\boxed{\star{\sf{\blue{ Angle _{1}+Angle_{2}+Angle_{3}=\:180^{⁰}}}}}}$

• $\frak{Here\: -:} \begin{cases} \sf{Angle_{1}= 3x}& \\\\ \sf{Angle _{2}= 5x}& \\\\ \sf{ Angle _{3}=7x}\end{cases}$

• $\star {\bigstar {\sf{\large { Now\: -: }}}}$

• $\longrightarrow{\sf{\large {3x+5x+7x=\:180^{⁰}}}}$

• $\longrightarrow{\sf{\large {8x+7x=\:180^{⁰}}}}$

• $\longrightarrow{\sf{\large {15x=\:180^{⁰}}}}$

• $\longrightarrow{\sf{\large {x=\:\dfrac{180}{15}}}}$

• $\longrightarrow{\sf{\large {x=\:12}}}$

$\star {\bigstar {\sf{\large { Therefore \: -: }}}}$

• $\boxed{\sf{\large {x=\:12}}}$

$\star {\bigstar {\sf{\large { Then\: -: }}}}$

• $\frak{Putting \:x=12 -:} \begin{cases} \sf{Angle_{1}= 3x=3 \times 12 = 36^{⁰}}& \\\\ \sf{Angle _{2}= 5x=12 \times 5 = 60^{⁰}}& \\\\ \sf{ Angle _{3}=7x= 7 \times 12 = 84^{⁰}}\end{cases}$

$\star {\bigstar {\sf{\large { Hence \: -: }}}}$

• $\underline{\boxed{\star{\sf{\blue{ The\:measure \:of\:the\:angles \:of\:triangles\:is\:36^{⁰},\:60^{⁰}\:and\:84^{⁰}}}}}}$

________________________________________

$\dag{\underline {\sf{\huge { ♡Verification-: }}}}$

• $\dag{\underline {\sf{\large { As\:we\:know\:that\: -: }}}}$

• $\underline{\boxed{\star{\sf{\blue{ Angle _{1}+Angle_{2}+Angle_{3}=\:180^{⁰}}}}}}$

• $\frak{Here\: -:} \begin{cases} \sf{Angle_{1}= 36^{⁰}}& \\\\ \sf{Angle _{2}= 60^{⁰}}& \\\\ \sf{ Angle _{3} = 84^{⁰}}\end{cases}$

• $\star {\bigstar {\sf{\large { Now\: , Putting\:known\:values\:-: }}}}$
• $\longrightarrow{\sf{\large {36+60+84=\:180^{⁰}}}}$

• $\longrightarrow{\sf{\large {36+144=\:180^{⁰}}}}$

• $\longrightarrow{\sf{\large {180^{⁰}=\:180^{⁰}}}}$

$\star {\bigstar {\sf{\large { Therefore \: -: }}}}$

• $\longrightarrow{\sf{\large {LHS=RHS}}}$

• $\longrightarrow{\sf{\large {Hence,\:Verified}}}$

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