Skill: Identify and measure angles

An angle is the amount of turn between two rays that share an endpoint. The shared endpoint is the vertex. The two rays are the sides of the angle.

Angles are named with three letters, with the vertex in the middle. For example, in $\angle ABC$, point $B$ is the vertex, and the sides are $\overrightarrow{BA}$ and $\overrightarrow{BC}$.

To measure an angle:

1. Place the center point of the protractor on the vertex.
2. Line up one side of the angle with the protractor’s $0^\circ$ line.
3. Read the number where the other side crosses the curved scale.
4. Use the scale that starts at $0^\circ$ on the side you lined up.

Example: Measure and classify $\angle ABC$.

Suppose ray $\overrightarrow{BA}$ is lined up with the protractor’s $0^\circ$ line, and ray $\overrightarrow{BC}$ crosses the scale at $65^\circ$.

• The measure is $\boxed{65^\circ}$.
• Since $65^\circ$ is less than $90^\circ$, the angle is acute.

So, $\angle ABC$ measures $\boxed{65^\circ}$ and is an acute angle.

Remember that the lengths of the rays do not change the angle’s measure. Only the amount of turn between the two rays matters.