Question

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Answer 1

`\begin{gathered} A=10x+22 \\ B=\text{ }11x+5 \\ C=13x-17 \\ \text{A+B+C}=180 \\ 10x+22+\text{ }11x+5+13x-17=180 \\ (10x+11x+13x)+(22+5-17)=180 \\ 34x+10=180 \\ 34x=180-10 \\ 34x=170 \\ x=(170)/(34) \\ x=5 \\ \text{The value of x is 5} \\ First\text{ find the angles} \\ A=10x+22 \\ A=10(5)+22 \\ A=72 \\ B=\text{ }11x+5 \\ B=\text{ }11(5)+5 \\ B=60 \\ C=13x-17 \\ C=13(5)-17 \\ C=48 \\ \text{The longest side is opposite the longest angle. } \\ \text{The longest angle is A=72, so the longest side is the segment }BC \end{gathered}`