The equation of the bisector of the obtuse angle between the lines x-y+2=0, 7x+y+1=0 is

Given lines x-y+2=0

$a_1=1, b_1=-1, c_1=2$

and

$$\begin{gathered} 7x+y+1=0 \\ {a}_2=7, b_2=1, c_2=1 \end{gathered}$$

Now

$a_1{a}_2+b_1{b}_2=1\left(7\right)+(-1)\left(1\right)=7-1=6>0$

The obtuse angle bisectors is 

               $\frac{a_{1}x+b_{1}y+c_1}{\sqrt{{a_1}^2+{b_1}^2}}=\frac{a_{2}x+b_{2}y+c_2}{\sqrt{{a_2}^2+{b_2}^2}}$

$\begin{array}{l}\Rightarrow \frac{x-y+2}{\sqrt{1+1}}=\frac{7x+y+1}{\sqrt{49+1}}\\ \Rightarrow \frac{x-y+2}{\cancel{\sqrt{2}}}=\frac{7x+y+1}{5\cancel{\sqrt{2}}}\\ \Rightarrow 5x-5y+10=7x+y+1\\ \Rightarrow 2x+6y-9=0\end{array}$