In a 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…

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