Understand the idea.
A right angle is a useful benchmark
An angle describes a turn between two rays meeting at a vertex. Use a square corner as a benchmark for a right angle, which is a quarter turn. Compare the marked opening with that corner, not with the lengths of the rays.
An acute angle is smaller than a right angle. An obtuse angle is larger than a right angle but smaller than a straight angle. An opening exactly equal to a square corner is right, rather than acute or obtuse.
Beyond a right angle
A straight angle is a half turn: its rays point in opposite directions along a straight line. A reflex angle is larger than a half turn and smaller than a full turn. Pay attention to which opening has been marked.
The same two rays have an opening on each side. The marked turn tells you which one to name. Extending the rays makes the arms longer, but it does not change their directions or the amount of turn.
See the method in action.
A narrow opening
The marked opening is smaller than a square corner. What type of angle is it?
Worked solution
- 1
Choose the benchmark.
A square corner shows the right-angle opening for comparison.
- 2
Compare the marked opening.
The supplied opening is smaller than the square corner, so it is less than a right angle.
- 3
Name the angle.
An opening smaller than a right angle is acute.
Acute.
A wide opening
An angle is bigger than a right angle but smaller than a straight angle. Name it.
Worked solution
- 1
Compare with a right angle.
The question states that the opening is bigger than a right angle.
- 2
Compare with a straight angle.
The opening is smaller than a straight, half-turn angle.
- 3
Name the angle between those benchmarks.
An angle larger than right and smaller than straight is obtuse.
Obtuse.
Try it yourself.
Check your understanding
What is the name of a half-turn angle?
Show answer & reasoning
A straight angle.
A half-turn angle is a straight angle. The rays point in opposite directions along one straight line: .
Keep practising
6 worksheet questions · 8 marks
Read the questions online
- Name the supplied narrow angle.1 mark
- Name a quarter-turn angle.1 mark
- Name the supplied wide angle.1 mark
- An opening is more than a half turn but less than a full turn. Name it.1 mark
- Two angles have equal openings but one has longer rays. Which angle is larger?2 marks
- Draw an acute angle and an obtuse angle. Label each.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Name the supplied narrow angle.1 mark
Its opening is less than a right angle.
Acute. - Name a quarter-turn angle.1 mark
A quarter turn matches a square corner.
A right angle. - Name the supplied wide angle.1 mark
It is larger than a right angle but smaller than a straight angle.
Obtuse. - An opening is more than a half turn but less than a full turn. Name it.1 mark
Reflex angles are larger than straight angles.
Reflex. - Two angles have equal openings but one has longer rays. Which angle is larger?2 marks
Ray length does not change the turn.
Neither; they are equal. - Draw an acute angle and an obtuse angle. Label each.2 marks
Use a paper corner to check the comparison; no protractor is needed.
Any acute opening smaller than a right angle and any obtuse opening between a right and straight angle.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Composite shapes/objects; angle names; reflection/rotational symmetry; creating designs.
Official curriculum source ↗