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Learn Index · Geometry and Spatial Reasoning Grade 3–5

Angles and angle measurement

An angle is the turn between two rays, measured in degrees.

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What is an angle?

An angle is formed when two rays (called arms) meet at a point called the vertex. The size of the angle is the amount of turn from one arm to the other.

Angles are measured in degrees (°). A full turn is 360°.

Types of angles

Type Size Picture
Acute angle less than 90° a narrow V
Right angle exactly 90° a square corner
Obtuse angle between 90° and 180° a wide, open angle
Straight angle exactly 180° a straight line
Reflex angle between 180° and 360° more than a half turn
Full turn 360° all the way around

Benchmarks

Turn Degrees
quarter turn 90°
half turn 180°
three-quarter turn 270°
full turn 360°

Compare an angle with a right angle (the corner of a page) to estimate it.

Using a protractor

A protractor has two scales: one running clockwise and one counterclockwise.

  1. Put the centre mark of the protractor exactly on the vertex.
  2. Line up the zero line (baseline) with one arm.
  3. Find where the other arm crosses the scale.
  4. Read the scale that starts at 0 on your first arm.
  5. Check: does your answer match the type? An acute angle must be less than 90°.

Drawing an angle

To draw 65°:

  1. Draw a straight arm and mark the vertex.
  2. Place the protractor centre on the vertex, baseline along the arm.
  3. Using the scale that starts at 0 on your arm, mark 65.
  4. Join the mark to the vertex.

Naming angles

An angle can be named by its vertex (∠B) or by three points with the vertex in the middle (∠ABC).

Worked examples

Example 1: Classify a 120° angle.

Between 90° and 180°: obtuse.

Example 2: How many degrees in a three-quarter turn?

3 × 90° = 270°.

Example 3: A protractor shows an arm at 40 on one scale and 140 on the other. The angle is clearly narrow. Which is correct?

Narrow means acute: 40°.

Common mistakes

  • Reading the wrong scale on the protractor. Start from 0 on your first arm.
  • Not placing the centre exactly on the vertex.
  • Thinking longer arms mean a bigger angle. Arm length doesn’t matter; only the turn does.

Try it yourself

  1. Classify 89°.
  2. Classify 180°.
  3. How many right angles make a full turn?
  4. What is the angle between the hands of a clock at 3:00?

Answers: 1) acute 2) straight 3) 4 4) 90°

Quick recap

  • An angle is the turn between two arms at a vertex, measured in degrees.
  • Acute < 90°, right = 90°, obtuse between 90° and 180°.
  • Use a protractor carefully: centre on the vertex, read from 0.