Determine the size of the acute angle, to the nearest degree, that is created by the intersection of the lines x=3 and 5x-10y+20=0.

The slope of a straight line is the tangent of the angle
made with the positive x-axis. To find the angle between two lines we can find the
difference of their slope and take the arc tan of the value we
get.

Here, we have two lines x = 3, this is a vertical line
that is perpendicular to the positive x-axis. As the slope of this line is infinite it
wouldn't be possible to find the difference of slopes. Instead, we can use the following
procedure.

The second line 5x - 10y + 20 =
0

=> 10y = 5x +
20

=> y = x/2 + 2

This
gives the slope as 1/2.

The angle that the line 5x - 10y +
20 = 0 makes with the positive x-axis is arc tan (1/2) = 26.565
degrees.

The angle that it would make with the vertical
line x = 5 is 90 - 26.565 = 63.43 degrees or 63
degrees.

The required angle created when the
two lines intersect is 63 degrees.