Question

14. The anges of a tiangde are in the ratio 5:4:3. Find measure of each angle​

Answer 1

Answer:

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Answer 2

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${\huge{\underline{\underline{\color{red}{\bf{Question}}}}}}$

The angle of a triangle are in ratio 5:4:3 find the three angle.

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${\huge{\underline{\underline{\color{green}{\bf{Answer}}}}}}$

$\sf{1st\:angle=75^o}$

$\sf{2nd\:angle=60^o}$

$\sf{3rd\:angle=45^o}$

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• To Find-All Three angles by the help of Ratio

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

• Ratio of Angles=5:4:3

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${\large{\underline{\underline{\bf{Explaination:}}}}}$

Let the Ratio as 5x.4x and 3x

${\large{\underline{\underline{\color{red}{\bf{Angle\:Sum\:Property\:of\:triangle:}}}}}}$

• Sum of all angles of triangle will always equal to $\rm{180^o}$

${\therefore{\underline{\sf{5x+4x+3x=180^o}}}}$

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${\quad{\qquad{\qquad{\sf{5x+4x+3x=180^o}}}}}$

${\quad{\qquad{\qquad{\sf{9x+3x=180^o}}}}}$

${\quad{\qquad{\qquad{\sf{12x=180^o}}}}}$

${\quad{\qquad{\qquad{\sf{12x=180^o}}}}}$

${\quad{\qquad{\qquad{\sf{x=\frac{180}{12} }}}}}$

${\quad{\qquad{\qquad{\boxed{\color{red}{\sf{x=15}}}}}}}$

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${\large{\underline{\underline{\color{blue}{\bf{Answer}}}}}}$

${\large{\sf{5x=5\times 15:\implies 75}}}$

${\large{\sf{4x=4\times 15:\implies 60}}}$

${\large{\sf{3x=3\times 15 :\implies 45}}}$

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${\large{\underline{\underline{\color{orange}{\bf{Confirming:}}}}}}$

${\large{\sf{Put\:all\:values\:In\:place\:of\:ratio}}}$

${\large{\sf{75^o+60^o+45^o=180^o}}}$

${\large{\sf{135^o+45^o=180^o}}}$

${\large{\sf{180^o=180^o}}}$

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${\large{\rm{Hence,Proved\:The\:one\:angle\:is\:75°,\:second\:angle\:is 60°\:and\:third\:angle\:is\:45°}}}$

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