What is the acute angle between the lines y - 12 = 0 and 2x - 2y + 98 = 0

We have to determine the angle between the lines y - 12 =
0 and 2x - 2y + 98 = 0.

We see that y -12 = 0 is a
horizontal line. It forms an angle of 90 degrees with the x
axis.

The slope of a line is the tangent of the angle it
forms with the positive x-axis.

2x - 2y + 98 =
0

=> y = x + 49

The
slope here is 1.

This implies that the line forms an angle
arc tan 1 with the positive x-axis.

arc tan 1 = 45
degrees

Using the angles formed by the lines with the
x-axis we get the angle between them as 90 - 45 = 45
degrees.

The acute angle between the given
lines is 45 degrees.