Question

if one angle of a parallelogram is two fifth of its adjacent angles find the angles of a parallelogram

Answer 1

Dear student,
$$\begin{gathered} L\mathrm{et}\mathrm{one}\mathrm{angle}\mathrm{be}x \\ \mathrm{and}\mathrm{another}\mathrm{angle}\mathrm{be}\frac{2x}{5} \\ weknowsumofadjacentpairofparalle\log ramis180° \\ \Rightarrow x+\frac{2x}{5}=180° \\ \Rightarrow \frac{5x+2x}{5}=180° \\ \Rightarrow \frac{7x}{5}=180° \\ \Rightarrow x=\frac{180°\times 5}{7} \\ \Rightarrow x=\frac{900°}{7} \\ \Rightarrow x=128.57° \\ thusoneangle=128.57° \\ andanotherangle=\frac{2\times 128.57°}{5}=51.42° \\ Asweknowopp.anglesofparalle\log ramaresamesotheanglesare \\ 128.57°,51.42°,128.57°,51.42° \end{gathered}$$
Regards