The line through the points (-1, 6) and (5, -2)intersects the line through (4, -4) and (1,7).Determine the angle between these two intersecting lines.

Answer 1

slope of 1st line = (-2-6)/(5+1) = -8/6 = -4/3
slope of 2nd line = (7+4)/(1-3) = -11/2

angle made by 1st line = tan^-1 (-4/3) = 126.87°
angle made by 2nd line = tan^-1 (-11/2) = 100.30°

angle between them = 26.565°

or

tan(angle between) = (-4/3 + 11/2)/(1 + (-4/3)(-11/2))
= (25/6) / (25/3) = 1/2
angle between = tan^-1 (1/2) = 26.565°