Angles and the protractor

Step 6 · Long division and equivalent fractions topics

See an angle as a turn measured in degrees, measure and draw angles with a protractor, and add angles that sit side by side.

What an angle is

An angle is made by two rays that start at the same point, the vertex. Its size is how far one ray turns to reach the other, measured in degrees (°). A full turn is 360°.

Two rays from one vertex make a right angle, 90°: a quarter of a full turn.

A quarter turn is 90°, a right angle, like the corner of a page. A half turn is 180°, a straight line.

Name	Size
Acute	Less than 90°
Right	Exactly 90°
Obtuse	Between 90° and 180°
Straight	Exactly 180°

Measuring with a protractor

A protractor is a half circle marked from 0° to 180°. Put its center on the vertex and line up the 0° mark with one ray. Read the scale where the other ray crosses it.

Most protractors have two scales, one running each way. Use the scale that starts at 0° on the ray you lined up. A quick check helps: an acute angle must read less than 90°.

An angle of 45°: half of a right angle.

Example: Reading the right scale

One ray lies along 0° on the inner scale. The other ray crosses the scales at 50° and 130°. How big is the angle?

The inner scale starts at 0° on the first ray, so read the inner scale.
The angle is smaller than a right angle, so it is acute.
50° fits; 130° would be obtuse.

Answer50°

Adding angles

When angles sit side by side with no gap and no overlap, the whole angle is the sum of the parts. That lets you find a missing angle.

Example: A missing angle

A right angle is split into two angles. One is 35°. How big is the other?

The two parts make 90°.
90° − 35° = 55°.

Answer55°

Example: On a straight line

Two angles sit side by side on a straight line. One is 110°. What is the other?

A straight line is 180°.
180° − 110° = 70°.

Answer70°

One degree is one 360th of a full turn. That is why a full turn is 360°, a half turn 180° and a quarter turn 90°.

Try it yourself

Work each one on paper first, then open the answer to check.

Is a 120° angle acute, right or obtuse?
Show answer
Obtuse. It is between 90° and 180°.
How many degrees are in a quarter turn?
Show answer
90°.
A 90° angle is split into two parts. One part is 62°. How big is the other?
Show answer
28°.
Two angles sit on a straight line. One is 45°. What is the other?
Show answer
135°.
Angles of 30°, 40° and 50° sit side by side. How big is the whole angle?
Show answer
120°.