Find the angles between each of the following pairs of straight lines :

x – 4y = 3 and 6x – y = 11

Given:


The equations of the lines are


x − 4y = 3 … (1)


6x − y = 11 … (2)


To find:


Angles between two lines.


Explanation:


Let m1 and m2 be the slopes of these lines.


m1m2 = 6


Let θ be the angle between the lines.
Then,



⇒


Hence, the acute angle between the lines is


1