Question

angles D and M are supplementary angles. angle D measures (3×+80) and angle M measures (2×-10) . what is measure of angle D?

Answer 1

Supplementary angles are two angles whose sum is exactly 180, therefore:

`\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=(110)/(5) \\ x=22 \end{gathered}`

Therefore:

`\begin{gathered} m\angle D=3x+80 \\ m\angle D=3(22)+80 \\ m\angle D=146 \end{gathered}`