Answer
[tex]\frac{12}{\sin\alpha}=\frac{x+2}{\sin \beta}[/tex]
and
[tex]\frac{8}{\sin180-\alpha}=\frac{x}{\sin \beta}[/tex][tex]\begin{gathered} \frac{12}{8}=\frac{x+2}{x} \\ \text{Cross multiply} \\ 12x=8x+16 \\ collect\text{ the like terms} \\ 12x-8x=16 \\ 4x=16 \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{16}{4} \\ \\ x=4 \end{gathered}[/tex]
The final answer
[tex]x=4[/tex]
