Answer:
63°.
Step-by-step explanation:
To find the angle we can use as limits of the figure the intersection of y = 2x-4 with the x-axis and any point at the right of it.
To find the intersection of y = 2x-4 with the x-axis we do y=0:
0 = 2x-4
4 = 2x
x = 4/2 = 2.
Then, the left limit is (2,0). Now, let's use x=3 as an example to find the right limit:
y = 2(3)-4
y = 6-4
y = 2.
Then, the right limit is (3,2). You can see it in graph below. As you can see, the acute angle [tex]\alpha[/tex] we are searching for can be calculated with the horizontal and vertical distances of the triangle limited by the two points, the line and the x-axis. So,
[tex]tan(\alpha) = \frac{2}{1}[/tex]
[tex]tan(\alpha) = 2[/tex]
[tex]\alpha = tan^{-1}(2)[/tex]
[tex]\alpha = 63.43\textdegree \approx 63\textdegree[/tex].
