Detailed Answer :
Let L1 and L2 be two non-vertical lines with slopes m1 and m2, respectively. If a1 and a2 are the inclinations of lines L1 and L2, respectively. Then m1 = tan θ1 and m2 = tan θ2
We know that when two lines intersect each to other, they make two pairs of vertically opposite angles such that sum of any two adjacent angle is 180°. Let q and f be the adjacent angles between lines L1 and L2 (sec fig). Then
positive and tan f will be – ve, which means ϕ will be acute and ϕ will be obtuse.
negative and tan ϕ will be positive, which means that ϕ will be obtuse and f will be acute.
Thus, the acute angle (sayq) between lines L1 and L2 with slopes m1 and m2, respectively is given by.
