Reading the inner and outer scale
Most protractors carry two sets of numbers around the arc, one running left to right and one running right to left. They exist so you can measure an angle opening from either side without flipping the tool. They are also the single most common reason a reading comes out wrong. Here is the simple rule that tells you which scale to trust every time.
Two scales, opposite directions
Look closely at the arc of a protractor and you will usually see two rows of numbers. One runs from zero up to 180 going one way; the other runs from zero up to 180 going the other way. They are not a mistake or decoration. They let you measure an angle that opens to the left or to the right without flipping the tool over.
A protractor "has degrees marked clockwise from 0 to 180 in the outer scale and anti-clockwise from 0 to 180 in the inner scale," and the two readings for any angle "add up to 180."
Source: Cuemath, Protractor: https://www.cuemath.com/geometry/protractor/"A protractor has two scales to allow angle measurement in both clockwise and anticlockwise directions. This avoids flipping the protractor."
Source: Vedantu, Protractor scale: https://www.vedantu.com/maths/protractor-scaleThe rule that always works
Read the scale whose zero sits on the arm you lined the baseline up with, and follow that same scale all the way round to the second arm. That is the whole trick. If your reference arm sits on the outer zero, the answer is on the outer numbers. If it sits on the inner zero, read the inner numbers.
The two scales exist precisely so one of them always starts at zero on your arm, whichever way the angle opens. Pick that one and ignore the other.
A sense check for the common mistake
Because the two numbers under the second arm always add up to 180, it is easy to read 60 as 120 or the other way round. A two-second sanity check catches it: a sharp, narrow angle is less than 90 degrees, and a wide, open one is more than 90. If the angle clearly looks narrow but you read 120, you are on the wrong scale.
Once you can read either scale confidently, the rest is just placement, covered in how to use a protractor. You can also turn the double scale on or off in the protractor tool if you prefer a single clean set of numbers.