Straight Lines And Pair Of Straight Lines

In a \(\triangle A B C\), suppose \(y=x\) is the equation of the bisector of the angle \(B\) and the equation of the side \(A C\) is \(2 x-y=2\). If \(2 A B=B C\) and the points \(A\) and \(B\) are respectively \((4,6)\) and \((\alpha, \beta)\), then \(\alpha+2 \beta\) is equal to