Instead of "angle", it's better to use slope or value change. Since the distance between each bar is constant at "1", the vertical change is all that is needed for a meaningful value. The angle on the chart is actually an illusion -- if you resize the chart, you can make the MA segment look very inclined or very flat.
Try this indicator: MA Slope, it might do what you are looking for. You can set the MA Period parameter, then it draws a histogram of the MA's change in value from bar to bar. Also, you can smooth the histogram with the MA Slope Period parameter.
Instead of an angle like 45 degrees, it will give you a pip value, like "the 14 MA value rises by 3.8".
Edit -- Doh!! I thought I had attached the indicator earlier, let me try again ...