Skill: Measure angles with a protractor

An angle measures how much one ray turns from another ray. We measure angles in degrees, written with the symbol $(^{\circ})$.

A protractor has:

• A small center mark
• A straight baseline
• Two number scales, each starting with $(0^\circ)$ on a different side

Steps for measuring an angle

1. Place the protractor’s center mark exactly on the angle’s vertex.
2. Line up one ray of the angle with the protractor’s baseline.
3. Find the scale that starts with $(0^\circ)$ on the ray you lined up.
4. Follow that scale until it reaches the second ray.
5. Read the angle measure and write it with a degree symbol.

Worked example

Suppose we want to measure $\angle ABC$. The vertex is $B$, and ray $(BA)$ is the bottom ray.

1. Place the protractor’s center mark on point $B$.
2. Line up ray $(BA)$ with the protractor’s baseline.
3. Since ray $(BA)$ points to the right, use the scale that begins with $(0^\circ)$ on the right side.
4. Ray $(BC)$ lines up with $(60)$ on that scale.
5. Therefore,

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

The other scale may show $(120^\circ)$ at the same spot, but that is the wrong scale because it does not start at $(0^\circ)$ on ray $(BA)$. Always begin reading from the $(0^\circ)$ mark on the ray you aligned with the baseline.