The angles in a right triangle are 5x-3 , 9x , 3x+13 , show that the triangle is right angled

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asked Oct 3, 2024 158k views

1 Answer

JonasG · Answer 1 · 2024-10-09T07:54:25+0000

It’s given, the angles in a right triangle are 5x-3 , 9x , 3x+13 . We have asked to prove that the given triangle is a right-angled triangle.

$\small \underline{ \boxed{ \sf{ \bigg(5x-3\bigg)°+\bigg(9x\bigg)°+\bigg(3x+13\bigg)°= 180° }}}\\$

$\sf \because\underline{ \:The\: three \:interior \:angles \:of \:any \:triangle \:add \:up \:to\: \red{180°}}\\$

$\:\:\:\:\:\:\longrightarrow \sf { \bigg(17x +10 \bigg)°= 180°}\\$

$\:\:\:\:\:\:\longrightarrow \sf { \bigg(17x\bigg)°= 180°-10°}\\$

$\:\:\:\:\:\:\longrightarrow \sf { \bigg(17x\bigg)°= 170°}\\$

$\:\:\:\:\:\:\longrightarrow \sf {x = (170°)/(17°)}\\$

$\:\:\:\:\:\:\longrightarrow \sf {x = (17°* 10°)/(17°)}\\$

$\:\:\:\:\:\:\longrightarrow \sf {x = \frac{\cancel{17°}* 10°}{\cancel{17°}}}\\$

$\:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{x =10°}}}}\\$

$\underline{\rm{\sf 1st\:Angle:-}}$

$\sf\longrightarrow \bigg(5x-3\bigg)° = \bigg(5* 10 -3 \bigg)°=\underline{ \pink{47°}}\\$

$\underline{\rm{\sf 2nd\:Angle:-}}$

$\sf \longrightarrow 9x° =\bigg( 9* 10\bigg)° =\boxed{\underline{\pink{90°}}}\\$

$\underline{\rm{\sf 3rd\:Angle:-}}$

$\sf \longrightarrow \bigg(3x+3\bigg)° =\bigg( 3* 10+13 \bigg)°= \underline{\pink{43°}}\\$

Since, one of the angles is 90°,henceforth we can say that the given triangle is a right-angled triangle.

$\:\:\:\:\:\:\\ \underline{ \cal{ \pmb{ \: \frak{\purple{Proved! \: }. }}}}\\$