Supplementary angles are two angles whose sum is exactly 180, therefore:
[tex]\begin{gathered} m\angle D+m\angle M=180 \\ \mleft(3x+80\mright)+\mleft(2x-10\mright)=180 \\ add_{\text{ }}like_{\text{ }}terms\colon \\ 5x+70=180 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 5x=110 \\ x=\frac{110}{5} \\ x=22 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m\angle D=3x+80 \\ m\angle D=3(22)+80 \\ m\angle D=146 \end{gathered}[/tex]