Skill: Measure angles in degrees

An angle measures how much one ray turns to reach another ray. The point where the rays meet is the vertex.

To measure an angle with a protractor:

1. Put the protractor’s center point exactly on the vertex.
2. Line up one ray with the protractor’s baseline, the line marked $0^\circ$.
3. Find the scale that starts at $0^\circ$ along that ray. Protractors have two scales, so use the correct one.
4. Read the number where the other ray crosses the protractor.
5. Measure to the nearest whole degree.

Example

Suppose the angle has a vertex at point $A$. One ray goes straight to the right, and the other ray slants upward. We want to measure $\angle A$.

• Place the center of the protractor on point $A$.
• Line up the ray going to the right with the protractor’s $0^\circ$ line.
• Since the baseline ray points right, use the scale that begins with $0^\circ$ on the right side.
• The slanted ray crosses the protractor at $65^\circ$.

Therefore,

$$m\angle A = 65^\circ$$

The length of either ray does not change the angle measure. Only the amount of turn between the rays matters. A right angle is $90^\circ$, a straight angle is $180^\circ$, and a full turn is $360^\circ$.