Angle of intersection

ritula wrote:CAn any1 tell - how 2 find angle of intesection of two lines byknowing the slopes of two lines?

Ian Stewart wrote:You actually can find the angle between any two lines if you know their slopes, but for the GMAT, you would only ever need to know how to identify perpendicular and parallel lines. As Morgoth points out, if one line has a slope of m, a perpendicular line will have a slope of -1/m.

If you want to find the angle of intersection between two arbitrary lines, you need to use trigonometry, which is definitely *not* tested on the GMAT. But, if you're really interested to know (and anyone who only wants to learn math for the GMAT- please stop reading here! ), let's take two lines that meet at point P = (x,y), and let's say they have positive slopes m and n where m > n. Recall what a slope means: if a line has slope m, that means if you go right by one, the line rises by m. So if you draw a horizontal line passing through P, you can make a right triangle with the following three points:

P = (x,y)
Q = (x+1, y)
R = (x+1, y + m)

where P and R are both on the line with slope m. From this triangle, if you remember trigonometry, you can see that the line with slope m has an angle of tan^(-1)[m] with the horizontal line. Similarly, the other line will make an angle of tan^(-1)[n] with the horizontal line, and the angle between the two lines will be the difference of these two angles: tan^(-1)[m] - tan^(-1)[n], assuming m > n. This can be extended for other cases (negative slopes, and the case where m < n), but this is the basic idea.