Question

Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{adjacent}\mathrm{angle}s\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{supplementry}. \\ \mathrm{Hence},\left(3x+10\right)°and\left(3x-4\right)°\mathrm{are}\mathrm{supplementry}. \\ \left(3x+10\right)°+\left(3x-4\right)°=180° \\ 6x°+6°=180° \\ 6x°=174° \\ x=29° \\ \mathrm{First}\mathrm{angle}=\left(3\mathrm{x}+10\right)°=\left(3\times 29°+10°\right)=97° \\ \mathrm{Second}\mathrm{angle}=\left(3\mathrm{x}-4\right)°=83° \\ \mathrm{Thus},\mathrm{the}\mathrm{angles}\mathrm{of}\mathrm{the}\mathrm{parallelogram}\mathrm{are}97°,83°,97°\mathrm{and}83°. \end{gathered}$$