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

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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.**

The angle between two lines could be found using the formula:

tan x = (m2 -m1)/(1 + m1*m2)

m1 is the slope of the first line: y - 12 = 0 => y = 12 => m1 = 0

m2 is the slope of the 2nd line: 2x- 2y + 98 = 0

2y = 2x - 98

y = x - 49

m2 = 1

tan x = (1 - 0)/(1 + 1*0)

tan x = 1/1

tan x = 1

x = 45 degrees

**The angle between the given lines measures 45 degrees.**