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Year 4 Maths Angles

Straight, reflex & revolution angles

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Theory

Straight, reflex and revolution angles are the large angles in Year 4 maths. A straight angle is a half turn, a revolution is a full turn, and a reflex angle is bigger than a straight angle but smaller than a revolution. This page shows how to name these angles, how to count them in right angles and turns, and how to find the reflex angle on the outside of a corner. In Western Australia this is taught in Year 5. Curriculum: VC2M4M04 / AC9M4M04.

A straight angle is a half turn. Its two arms point in opposite directions and make a straight line. It is the same as 2 right angles.

A revolution is a full turn, all the way around back to the start. It is the same as 4 right angles, or 2 straight angles.

A reflex angle is bigger than a straight angle but smaller than a revolution. It is marked the long way round, with an arc that goes past the straight line.

Every corner has two angles: the one inside and the one outside. Together they make a revolution. If the inside angle is less than a straight angle, the outside angle is a reflex angle.

A straight angle and a revolution Left: two arms pointing opposite ways from a point, with a half-circle arc: a straight angle. Right: one arm with a full circle arc around its vertex: a revolution. straight angle revolution
A straight angle is a half turn. A revolution is a full turn.
A reflex angle and the angle inside it Two arms meet at a vertex. A small arc marks the sharp angle between them. A large red arc goes the long way round, marking the reflex angle. reflex angle (red)
The big red arc marks a reflex angle: more than a half turn, less than a full turn.
AngleHow much turnRight angles
Right anglea quarter turn1
Straight anglea half turn2
Reflex anglemore than a half turn, less than a full turnmore than 2, less than 4
Revolutiona full turn4

From smallest to largest: acute, right, obtuse, straight, reflex, revolution.

\[ \text{inside angle} + \text{outside angle} = \text{1 revolution} \]
No degrees needed. Name these angles by comparing them with a straight line and a full turn, and count them in right angles.

How to name a large angle

  1. Look at the arc. Find which way round the angle is marked.
  2. Compare with a straight line. If the arc is exactly a straight line, it is a straight angle. If it goes past the straight line, keep going.
  3. Compare with a full turn. If it goes all the way round to the start, it is a revolution. If it stops before that, it is a reflex angle.

How to count a turn in right angles

  1. Count quarter turns. Each quarter turn is 1 right angle.
  2. Name the fraction of a turn. 1 right angle is a quarter turn, 2 right angles a half turn, 3 right angles a three-quarter turn and 4 right angles a full turn.
  3. Use revolutions. Each full revolution is 4 right angles, so add 4 for every revolution.
Example 1 — Name the angles
Name each marked angle \(P\), \(Q\) and \(R\).
Three angles P, Q and R Angle P is marked the long way round with a big red arc. Angle Q is a straight line through its vertex. Angle R opens wider than a square corner but less than a straight line. P Q R
Solution

\(P\) is marked the long way round, past the straight line but not all the way round: a reflex angle.

\(Q\) is a straight line through its vertex: a straight angle.

\(R\) is wider than a square corner but less than a straight line: an obtuse angle.

Example 2 — The outside of a corner
The inside angle of a corner is obtuse. What type of angle is the outside angle of that corner?
Solution

The inside and outside angles together make a revolution.

An obtuse angle is less than a straight angle (a half turn), so the outside angle must be more than a half turn.

It is less than a full turn, so the outside angle is a reflex angle.

Example 3 — Count the right angles
A dancer spins through \(3\) whole revolutions. How many right angles is that?
Solution

\(1\) revolution \(= 4\) right angles.

\(4 + 4 + 4 = 12\), so \(3\) revolutions are \(12\) right angles.

Example 4 — A clock turn
The minute hand of a clock turns from 12 to 9, going the usual way round. Name the angle it turns through.
Solution

12 to 3 is a quarter turn, 3 to 6 is another and 6 to 9 is another: \(3\) right angles.

That is more than a half turn but less than a full turn, so the hand turns through a reflex angle.

Example 5 — Put them in order
Order these angles from smallest to largest: a straight angle, an acute angle, a reflex angle, a right angle.
Solution

Acute is less than a right angle, a straight angle is 2 right angles, and a reflex angle is more than a straight angle.

Order: acute, right, straight, reflex.

Common pitfalls

Check which way round. Two arms make two angles. Look at the arc to see whether the small angle or the reflex angle (the long way round) is marked.
A reflex angle is bigger than a straight angle. Watch out for thinking a reflex angle is small because its arms look close together. It is the angle the long way round.
A revolution is a whole turn. A revolution goes all the way round to the start. It is 4 right angles, not 2.

Frequently asked questions

How can I spot a reflex angle?

Look at the arc that marks the angle. If it goes past a straight line but does not go all the way round, the angle is reflex.

Why is a full turn called a revolution?

To revolve means to go around. A revolution is one whole trip around, back to where you started.

Does every corner have a reflex angle on the outside?

Every corner whose inside angle is less than a straight angle has a reflex angle on the outside, because the inside and outside angles together make a full turn. Two arms that make a straight line are different: both sides are straight angles, because 2 + 2 = 4 right angles.

Can you turn more than one revolution?

Yes. One and a half revolutions is a full turn and then a half turn more, which is \(4 + 2 = 6\) right angles.

Do I need degrees to name these angles?

No. You can name every angle by comparing it with a right angle, a straight line and a full turn.

What is the biggest type of angle?

A revolution, a full turn, is the biggest. Reflex angles are the next biggest, then straight angles.

More in Angles
Classify angles (acute, right, obtuse)
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