Theo t/c hình thang ta luôn có : \(\widehat{A}+\widehat{D}=180^0\) và \(\widehat{B}+\widehat{C}=180^0\)
Kết hợp với đề bài ta được :
\(\left\{{}\begin{matrix}\widehat{A}=3\widehat{D}\\\widehat{A}+\widehat{D}=180\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\widehat{A}=3\widehat{D}\\3\widehat{D}+\widehat{D}=180\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\widehat{A}=3\widehat{D}\\4\widehat{D}=180\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\widehat{A}=135^0\\\widehat{D}=45^0\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\widehat{B}+\widehat{C}=180\\\widehat{B}-\widehat{C}=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\widehat{B}+\widehat{C}=180\\2\widehat{C}=150\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\widehat{B}=105^0\\\widehat{C}=75^0\end{matrix}\right.\)
