Since the three angles are supplementary, their sum equals 180. Then, we can write the following equation:
[tex](x+2)+(2x+4)+(x-2)=180[/tex]solving for x, we get:
[tex]\begin{gathered} x+2+2x+4+x-2=180 \\ \Rightarrow4x+4=180 \\ \Rightarrow4x=180-4=176 \\ \Rightarrow x=\frac{176}{4}=44 \\ x=44 \end{gathered}[/tex]now that we have that x = 44, the measures of each angle are:
[tex]\begin{gathered} m\measuredangle1=44+2=46 \\ m\measuredangle2=2(44)+4=88+4=92 \\ m\measuredangle3=44-2=42 \end{gathered}[/tex]