 Start by placing the centre reticle of the protractor on top of the vertex of the angle, and aligning the reticle horizontal line with the base line of the angle.  Let's measure some angles: Example 1: 
The angle is measured from the right, counterclockwise, using the inner scale which starts at zero degrees. The angle is one notch under 40°, which makes it 39°. Example 2: 
This time we're using the outer scale, which starts at zero degrees on the left. We measure clockwise. The angle appears to be about 13°. Example 3: 
Try this one yourself. We're measuring from the right, using the inner scale. When you think you know the answer, hold your mouse cursor over the black square to see if you were correct. 
Example 4: In this example, the angle is reflex. Since our protractor only measures angles up to 180°, we'll need to turn it upside down and measure the extra amount x past 180°.
Now add this to 180° to get the total reflex angle of
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