Answer:
= 55.3 degrees
Explanation:
To find the supplementary angles formed by two lines, we need to find the angles formed by each line and then subtract the sum of those angles from 180 degrees.
Let's begin by finding the slope of each line. The first line y=3x-5 is in slope-intercept form,
where the slope is the coefficient of x, which is 3.
The second line 4x-3y=1 can be rearranged to slope-intercept form by solving for y:
4x - 3y = 1
-3y = -4x + 1
y = (4/3)x - 1/3
The slope of the second line is 4/3.
Next, we can find the angle formed by each line with the x-axis using the formula:
angle = arctan(slope)
where arctan is the inverse tangent function. We can use a calculator to find the angle in degrees.
For the first line, angle = arctan(3) ≈ 71.57 degrees.
For the second line, angle = arctan(4/3) ≈ 53.13 degrees.
To find the supplementary angles, we subtract the sum of these angles from 180 degrees:
supplementary angle = 180 - (71.57 + 53.13) = 55.3 degrees.
Therefore, the supplementary angles formed by the line y=3x-5 and the line 4x-3y=1 are 55.3 degrees.