Angle between two straight lines:
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If q is acute angle between the two lines, then
 where m1 and m2 are the slopes of the two lines and are finite.
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Notes:
- If the 2 lines are perpendicular to each other then m1m2 = -1.
- Any line perpendicular to ax + by + c = 0 is of the form bx - ay + k = 0.
- If two lines are parallel or are coincident, then m1 = m2.
- Any line parallel to ax + by + c = 0 is of form ax + by + k = 0.
- If any of the 2 lines is perpendicular to the x-axis, then slope of that line is not define (infinite).
or θ = |90° - a|, here tanα = m2 i.e. angle θ is the complimentary to the angle which oblique line makes with x-axis.
Illustration: Find equation to the sides of an isosceles right angled triangle, the equation of hypotenuse of which is x - 2y = 3 and the opposite vertex is the point (2, 2).
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Solution: Evidently other two sides of triangle will be making an angle of 45o with given line. That means we have to find out the equation of line passing through point (3, 2) and making an angle of 45o with given line. Slope of the given line x - 2y = 3 is m1 = 1/2.
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Hence required equations of two lines are
3x - y - 7 = 0 and x + 3y - 9 = 0
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