Question

A ABG - ASRG R 12 X G А S 14 36 B. AA ~; X=31 O SAS ~; X= 31 AA ~; X = 42 SAS - ; x = 42

Answer 1

∠AGB ≅ ∠RGS because they are vertical angles. Then, the two triangles are similar by AA postulate. Therefore, the next proportion must be satisfied,

`\begin{gathered} (BG)/(GR)=(AG)/(GS) \\ (36)/(12)=(x)/(14)_{} \end{gathered}`

Solving for x,

`\begin{gathered} 3=(x)/(14) \\ 3\cdot14=x \\ 42=x \end{gathered}`

Final answer: AA~; x = 42