How to represent percentages to degrees on a graph?

Question

I am trying to visually represent a percentage on a 4 quadrant graph with a line that is supposed to tilt with an angle.

For example:

Clockwise 4 quadrant graph.

  270*
180* 0*
  90*

I get a percentage back from my calculation: (b-a)/b. I need to represent this percentage on my graph by tilting the arrow with the correct angle.

For example 20-10/20 = 0.5 or 50% I would expect this to tilt to the right by 45*. Like this:

\

How can I convert my 50% to 45*?

Answer 1

Use proportions. If $x$ is the angle corresponding to $50\%$, then $$ \frac{x}{90} = \frac{50}{100} $$ By the way, this manner of measuring angles is referred to as gradians.