Compare angles to a right angle
Theory
Comparing angles to a right angle is a Year 4 maths measurement skill. A right angle is a square corner and a quarter turn, and we use it as a benchmark to decide whether an angle is less than, equal to, or greater than a right angle. This page also shows how to count right angles in shapes and how right angles link to turns and directions. In the Australian Curriculum and the Victorian Curriculum this is Year 3 content; it is taught in Year 4 in Western Australia. Curriculum: VC2M3M05 / AC9M3M05.
A right angle is a square corner, like the corner of this page or a book. It is the same amount of turn as a quarter turn. A right angle is marked with a small square marker in the corner.
We use the right angle as a benchmark to describe other angles. An angle can be less than a right angle (a narrow, sharp opening), equal to a right angle (exactly a square corner), or greater than a right angle (a wide opening).
The size of an angle is how much it opens, not how long the arms are. Two angles with the same opening are the same size, even if one has longer arms.
Right angles also measure turns. A quarter turn is 1 right angle, a half turn (a straight line) is 2 right angles and a full turn is 4 right angles.
These facts link the right angle to turns. Use them to compare angles and to count turns.
| Turn | Right angles |
|---|---|
| Quarter turn | 1 |
| Half turn (a straight line) | 2 |
| Three-quarter turn | 3 |
| Full turn | 4 |
How to compare an angle to a right angle
- Picture the square corner. Think of the corner of a page, or use one as a tester. That is exactly a right angle.
- Line up one arm. Put the corner of the paper at the vertex, with one edge along one arm of the angle.
- Read the opening. If the other arm cuts across the paper, the angle is less than a right angle. If it lies along the paper's other edge, it is equal. If it opens out past the paper's corner, it is greater than a right angle.
How to count right angles in a turn
- Count quarter turns. Each quarter turn is 1 right angle.
- Follow the directions. Turning right (clockwise) one quarter turn at a time goes north, east, south, west and back to north.
Angle \(R\) has the small square, so it is equal to a right angle.
Angle \(Q\) opens less than a square corner, so it is less than a right angle.
Angle \(P\) opens wider than a square corner, so it is greater than a right angle.
The shape has 6 corners. Check each one.
Five corners are square corners (marked with a small square). The inside corner of the L opens wider than a right angle.
The shape has \(5\) right angles.
Each right angle is a quarter turn to the next direction.
East \(\to\) south (1), south \(\to\) west (2), west \(\to\) north (3).
Kim now faces north. She has made a three-quarter turn.
The paper corner sticks out past the second arm, so the angle opens less than the square corner.
The angle is less than a right angle.
Angle \(D\) opens much wider than a square corner and angle \(F\) opens much less.
Angle \(E\) opens only a little less than a square corner, so \(E\) is closest to a right angle.
Common pitfalls
Frequently asked questions
What is a right angle?
A right angle is a square corner, like the corner of a page or a book. It is the same amount of turn as a quarter turn, and it is shown with a small square marker in the corner.
How do you compare an angle to a right angle?
Look at how far the arms open. If the opening is narrower than a square corner the angle is less than a right angle. If it opens the same it is equal to a right angle. If it opens wider it is greater than a right angle.
Can a small drawing of an angle be bigger than a large drawing?
Yes. The size of an angle is how much it opens, not how long the arms are. A small angle drawing that opens wide is bigger than a large drawing that opens only a little.
Can a triangle have two right angles?
No. If two corners of a triangle were square corners, the two other sides would both stand straight up and never meet, so the shape could not close. A triangle has at most one right angle.
How many right angles are in three-quarters of a turn?
Each quarter turn is one right angle, so three quarter turns are \(3\) right angles.
What does the small square in a corner mean?
The small square marker in a corner is the sign for a right angle. When you see it, the angle is exactly a right angle, so you do not need to guess by eye.