Question 1033779
The line through the points (4,1) and (2,-5) has a slope {{{m[2] = (1--5)/(4-2) = 3}}}, while the line through the points (-3,-5) and (x,-1) has slope {{{m[1] = (-1--5)/(x--3) = 4/(x+3)}}}.

Let {{{theta}}} be the positive, acute angle between the two lines.

==> {{{tan(theta) = (m[2]-m[1])/(1+m[2]*m[1]) = (3 - 4/(x+3))/(1+12/(x+3))}}}

==> {{{tan 45^o = 1 = (3x+5)/(x+15)}}}, after simplification.

==> x+15 = 3x+5 ==> 10 = 2x  ==> {{{highlight(x = 5)}}}.