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what acute angle between lines y x y

what acute angle between lines y x y
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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 + 49The slope here is 1.This implies that the line forms an angle arc tan 1 with the positive x-axis.arc tan 1 = 45 degreesUsing 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.
what acute angle between lines y x y

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 = 0m2 is the slope of the 2nd line: 2x- 2y + 98 = 02y = 2x – 98y = x – 49m2 = 1tan x = (1 – 0)/(1 + 1*0)tan x = 1/1tan x = 1x = 45 degreesThe angle between the given lines measures 45 degrees.