The equation of angular bisector of the lines 3x+4y+5=0  and 4x−3y+7=0  is lx+my+n=0 , which makes acute angle with  x-axis then the value of l+m+n  is

The equations of angular bisectors of  a1x+b1y+c1=0 and  a2x+b2y+c2=0 are   a1x+b1y+c1a12+b12=±a2x+b2y+c2a22+b22To get the equation of angular bisectors of two perpendicular lines, add both equations for one angular bisector and subtract one from the other for other angular bisector.Since the lines given are perpendicular to each otherThe angular bisector is 3x+4y+5+4x−3y+7=07x+y+12=0The other angular bisector is 3x+4y+5−4x−3y+7=03x+4y+5−4x+3y−7=0−x+7y−2=0x−7y+2=0Observing the above two angular bisectors, the slope of  x−7y+2=0 is positive, hence this makes acute angle with   x-axis. Therefore,   l+m+n=1−7+2=−4