Gọi góc phân giác góc B, D là góc B1, D1
\(\Rightarrow\) \(\widehat{\text{B1}}\)=\(\dfrac{\widehat{B}}{2}\), \(\widehat{\text{D1}} =\dfrac{\widehat{D}}{2}\)
Trong tứ giác ABID, có góc \(\widehat{\text{A}}+\widehat{B1}+\widehat{ BID}+\widehat{\text{D1}}\)=360
\(\Leftrightarrow\)\(\widehat{\text{A}}+\widehat{\dfrac{B}{2}}+\widehat{BID}+\dfrac{\widehat{\text{D}}}{2}\)=3600
\(\Leftrightarrow\)\(2\widehat{\text{A}}+\widehat{B}+\widehat{2BID}+\widehat{2\text{D}}\)=3600.2
\(\Leftrightarrow\) \(\widehat{B}+\widehat{D}\)= 720- \(2\widehat{\text{A}}+\widehat{2BID}\) (1)
Trong tứ giác ABCD ta có: \(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{\text{D}}\)=3600 (2)
Mà \(\widehat{A}-\widehat{C}\)=600
\(\Leftrightarrow\) A=60+C thay vào (2):\(60^0+\widehat{2C}+\widehat{B}+\widehat{D}=360^0\) (3)
Thay 1 vào 3, ta có: \(60^0+\widehat{2C}+720-2\widehat{A}+\widehat{2BID}=360^0\)
\(\Leftrightarrow\)600+7200 - 2.600-3600= \(\widehat{2BID}\)
\(\Leftrightarrow\) \(\widehat{2BID}\)= 1500
