∠AGB ≅ ∠RGS because they are vertical angles. Then, the two triangles are similar by AA postulate. Therefore, the next proportion must be satisfied,
[tex]\begin{gathered} \frac{BG}{GR}=\frac{AG}{GS} \\ \frac{36}{12}=\frac{x}{14}_{} \end{gathered}[/tex]
Solving for x,
[tex]\begin{gathered} 3=\frac{x}{14} \\ 3\cdot14=x \\ 42=x \end{gathered}[/tex]
Final answer: AA~; x = 42
