\(\left\{{}\begin{matrix}\widehat{A}=\frac{1}{3}\widehat{D}\\\widehat{B}-\widehat{C}=50^o\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\widehat{D}=3\widehat{A}\\\widehat{B}=\widehat{C}+50^o\end{matrix}\right.\)
+ AB // CD \(\Rightarrow\left\{{}\begin{matrix}\widehat{A}+\widehat{D}=180^o\\\widehat{B}+\widehat{C}=180^o\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\widehat{A}+3\widehat{A}=180^o\\2\widehat{C}+50^o=180^o\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}4\widehat{A}=180^o\\2\widehat{C}=130^o\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\widehat{A=45^o}\\\widehat{C}=65^o\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\widehat{D}=135^o\\\widehat{B}=115^o\end{matrix}\right.\)
