What is the angle of the slop of a line with gradient 1/2 and that of another perpendicular to it?

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops.

The equation of a line is y = mx where m is the slope. That line passes through the origin. If you want it to pass through some point (a, b) you subtract the coordinates like this: y - b = m(x - a). That is the point-slope form, and you can rewrite it in other forms if it is convenient. You may do this with any point on the line. They all reduce to the same equation.

To figure an angle you are getting into trigonometry and that involves a lot more memorization and holding pictures in your head. You need to learn the basics of algebra perfectly before you get into angles.

The slope of a line is the tangent of the angle it makes with the horizontal axis. If the slope is 1/2 then the angle is 26.56505118 degrees.

The perpendicular to a line has slope equal to the negative reciprocal. So the perpendicular to a slope of 1/2 has the slope -2 and the angle is -63.43494882 degrees.