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

Sagot :

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]

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