Identify angles in shapes & the environment
Theory
An angle is the amount of turn between two straight arms that meet at a point called the vertex. This Year 3 maths page shows how to name the vertex and arms, count the angles in shapes, spot angles in everyday objects, and compare and order angles by how wide they open. Curriculum: VC2M3M05 / AC9M3M05.
An angle is made from two straight arms that meet at a corner point. That corner point is the vertex. The size of an angle is the amount of turn between the arms, or how far they open apart.
A wide opening is a big angle and a narrow opening is a small angle. Making the arms longer does not change the angle, because only the opening matters, not the length of the arms.
Every corner of a shape is an angle. To count the angles in a shape, count its corners. Angles are also in everyday objects: the vertex is the point where the two parts join, like the hinge of a door, the pivot of a pair of scissors or the centre of a clock.
Every angle has 1 vertex and 2 arms. Every corner of a shape is one angle, so the number of angles in a shape is the same as its number of corners.
| Shape | Corners | Angles |
|---|---|---|
| Triangle | 3 | 3 |
| Quadrilateral (square, rectangle) | 4 | 4 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 6 |
| Octagon | 8 | 8 |
How to find and describe an angle
- Find the vertex. Look for the corner point where two straight arms meet. In an object, it is the point where the two parts join, like a hinge or a pivot.
- Follow the arms. The two arms reach out from the vertex. Every angle has exactly two arms.
- Look at the opening. The amount of turn between the arms is the size of the angle. A wider opening means a bigger angle.
How to compare several angles
- Ignore the arm lengths. Look only at how far each angle opens.
- Find the narrowest opening. That is the smallest angle. The widest opening is the largest angle.
- Put the rest in between. Line them up from the smallest opening to the largest.
The arms meet at \(M\), so \(M\) is the vertex.
The two arms go from \(M\) out to \(L\) and \(N\). An angle always has 2 arms.
Start at the top-left corner and go around, touching each corner once. Do not miss the inside corner of the L.
There are 6 corners, so the shape has \(6\) angles.
The covers meet at the spine, so the spine is the vertex.
As the book opens wider, the covers turn further apart, so the angle gets bigger.
Angle \(Y\) opens the least, so it is the smallest.
Angle \(Z\) opens the most, so it is the largest.
In order: \(Y\), \(X\), \(Z\).
No. The size of an angle is the opening, not the length of the arms.
Angle \(Q\) opens much wider than angle \(P\), so angle \(Q\) is the bigger angle.
Common pitfalls
Frequently asked questions
What is an angle?
An angle is made when two straight arms meet at a point. The size of the angle is the amount of turn between the arms.
What is the plural of vertex?
The plural of vertex is vertices. A shape with 5 corners has 5 vertices, and each vertex is the corner of one angle.
How do you count the angles in a shape with lots of corners?
Start at one corner and go around the shape, touching each corner once. Every corner is one angle, so a shape with 7 corners has 7 angles.
If you rule the arms of an angle longer, does the angle change?
No. Making the arms longer does not change how far they open apart, so the angle stays the same size.
How do you tell which angle is bigger?
Look at the opening between the arms. The angle with the wider opening is the bigger angle, and the angle with the narrower opening is the smaller one.
Where can you see angles in everyday life?
Angles are everywhere: the tip of a slice of pizza, an open book, a ladder leaning on a wall and the corner of a window all show angles.