Skill: Use a protractor to measure angles

An angle measures how wide the opening is between two rays. The lengths of the rays do not matter. A protractor measures angles from $(0^\circ)$ to $(180^\circ)$.

Steps for measuring an angle:

1. Place the protractor’s center point exactly on the angle’s vertex.
2. Line up one ray with the protractor’s $(0^\circ)$ baseline.
3. Find the scale that begins with $(0^\circ)$ on the ray you lined up.
4. Read the number where the other ray crosses the protractor.
5. Check your answer: an angle smaller than a right angle is less than $(90^\circ)$, and an angle larger than a right angle is greater than $(90^\circ)$.

Example

Suppose we want to measure $\angle ABC$, whose vertex is $B$.

1. Put the center mark of the protractor on point $B$.
2. Place ray $\overrightarrow{BA}$ along the protractor’s baseline pointing to $(0^\circ)$.
3. Ray $\overrightarrow{BC}$ crosses the protractor at $(60^\circ)$.
4. Read the scale that starts at $(0^\circ)$ along ray $\overrightarrow{BA}$, not the scale that starts at $(180^\circ)$ there.
5. Therefore,

$$m\angle ABC=60^\circ.$$

This makes sense because $(60^\circ)$ is less than $(90^\circ)$, so the angle should look narrower than a right angle.