7. The vertices of a triangle are $P(-8$, 5), $Q(-15,-19), R(1,-7), \angle P$ bisector can be expressed as $a x+2 y+c=0$, find $a+c$,


7. Extend $P R$ to $T$, such that $P Q=P T$. Since $P Q=25, P R=15$, then the coordinates of $T$ are $(7,-15)$, and the angle bisector intersects $Q T$ at the midpoint $(-4,-17)$.
Thus, the slope of the angle bisector is $-\frac{11}{2}$, and the equation is
$$
\begin{array}{r}
11 x+2 y+78=0 . \\
\text { Hence } a+c=11+78=89 .
\end{array}
$$