What is the angle between the lines x + y = 3 and x + 3y = 5?

x+y = 3. and x+3y = 5.

We write
both lines in the slope intercept form like y = mx+c, where m is the slope (tangent of the angle
with x axis) of the line and c is intercept of the line on y
axis.

x+y = 3 is written like: y =
-x+3.....(1)

x+3y = 5 is written in the form   y =
-(1/3)x+5/3....(2)

So the slope of the first line m1 = -1. and the
2nd line = m2 -1/3.

Therefore the angle between the lines  is given
by:

   tanA = (m1-m2)/(1+m1m2) =
(-1+1/3)/{1+(-1)(-1/3)}

tan A = {(-2/3)/((4/3)} = -2/4 =
-1/2.

Therefore A =  arc tan  (-1/2) =  -26.56 degre from line (1)
to line (2).

Or 26. 56 degree from line (2) to line
(1).