The two lines every protractor has
A semicircular protractor is built around two reference lines. The baseline is the straight bottom edge, printed flat and used to align one arm of the angle. The vertex mark is a small hole or crosshair at the centre of that straight edge, and it marks the exact point every angle on the protractor is measured from. Getting a reading right starts with both of these, before either number scale is even read.
Lining it up
Place the vertex mark exactly on the corner where the two lines of the angle meet. This is the single step most readings go wrong at: a vertex mark sitting even a millimetre off the true corner throws the reading off by a degree or more on a small protractor, proportionally worse the smaller the angle. Once the vertex is seated, rotate the protractor so its baseline lies exactly along one arm of the angle, with that arm pointing toward the 0° mark on whichever scale you plan to read.
With both lines aligned, the second arm of the angle crosses the curved edge of the protractor at the angle's measurement. Read the number where it crosses, and stop there, because which of the two printed numbers at that point is correct depends on the next section.
Inner scale or outer scale
Almost every protractor prints two rows of numbers along its curved edge: one running 0° to 180° left to right, the other running 180° to 0° in the same direction. They exist because an angle can open to the left or to the right depending on how it is drawn, and one row is built for each direction.
The rule that avoids the mistake: read the same scale you measured 0° from. If the first arm of the angle lines up with the outer scale's 0°, the second arm's reading comes from the outer scale too, not the inner one, even though the inner number sitting at the same physical point looks equally plausible. Reading the wrong scale is the single most common protractor error, and it produces a specific, recognisable mistake: a reading that is 180° minus the correct one.
Naming what you have measured
Once a reading is in hand, four names cover every case. An angle under 90° is acute. Exactly 90° is a right angle. Between 90° and 180° is obtuse. Exactly 180° is a straight angle, effectively a straight line. Beyond 180° and under 360°, an angle is reflex, and a standard semicircular protractor cannot measure one directly, since its scale stops at 180°.
Measuring a reflex angle
To find a reflex angle, measure the smaller angle on the other side of the same vertex, the one that is under 180° and reads normally, then subtract that number from 360°. An angle that looks close to a full turn but is not quite one, with a small gap of perhaps 40° on the near side, is a reflex angle of 320° (360 − 40).
Degrees and radians
Degrees split a full turn into 360 equal parts, a convention that goes back to Babylonian mathematics. Radians measure the same turn in a unit tied to the circle's own geometry, where one full turn is 2π radians, a straight angle is π radians, and a right angle is π/2. Converting between them is one multiplication: degrees × (π/180) gives radians, and radians × (180/π) gives degrees back. A 45° angle, for instance, is π/4 radians, close to 0.785.
The protractor on this site reads and displays both units at once, drawn to your screen's calibrated scale, so the arm can be checked against a real edge rather than trusted by eye alone.