You can use the Measure Tool in GIMP to get this information. Open your meter image with GIMP. Select the Measure Tool (it looks like a drawing compass) or select Tools->Measure. Click-and-hold the left mouse button on the pivot point and make a measurement straight down by the length of the needle. Release the click and get the needle’s zero point (angle). Now go back to the pivot point, hold the Shift key, click the left mouse button again, and move the pointer to the desired needle location. The Measure Tool will display the measured angle. Note: It will tend to keep the angle measurements less than 180 degrees, so you will need to do the math for larger angles.
GIMP documentation for the Measure Tool
See our video tutorial called “Design a Needle for the Meter Define Command.”