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goblinko [34]
3 years ago
7

Angle trs is a straight angle. andgle trx is a right angle. angle trs=2x+5y, angle xrs=3x+3y. solve for x and y

Mathematics
1 answer:
Simora [160]3 years ago
8 0

\bf \begin{cases}\stackrel{\measuredangle TRS}{2x+5y}=180\\2x=180-5y\\\boxed{x}=\frac{180-5y}{2}\\[-0.5em]\hrulefill\\\stackrel{\measuredangle XRS\cong \measuredangle TRX}{3x+3y}=90\end{cases}~\hspace{7em}\stackrel{\textit{using \boxed{x} in the second equation}}{3\left( \boxed{\frac{180-5y}{2}} \right)+3y=90}


\bf \cfrac{540-15y}{2}+3y=90\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{540-15y+6y=180}\implies -9y=-360\\\\\\y=\cfrac{-360}{-9}\implies \blacktriangleright y=40 \blacktriangleleft \\\\\\\stackrel{\textit{using \underline{y} in the first equation}}{2x+5(40)=180}\implies 2x+200=180\implies 2x=-20\\\\\\x=\cfrac{-20}{2}\implies \blacktriangleright  x=-10\blacktriangleleft


if you ever wonder why we multiplied by the LCD of 2, is just to do away with the denominators.

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