Classifying angles

Make an angle

Drag the orange dot to open and close the angle, or use the buttons. Watch how the name of the angle changes. Press Play and make the angles we ask for.

Drag the orange dot.

Angles are all around us: in the corner of a book, in a slice of pizza, between the hands of a clock. On this page you will learn what an angle is, how to tell a right angle from an acute, an obtuse and a straight angle, and how to check an angle with a corner folded from paper.

On this page: What is an angle? · Right angle · Acute angle · Obtuse angle · Straight angle · Which angle is bigger? · Angles in shapes · Angles on a clock · Degrees · Practice

What is an angle?

Draw two straight lines that start at the same point. Together they make an angle.

The point where the two lines start is the vertex of the angle. The two lines are the sides of the angle.

The small arc near the vertex shows which angle we are talking about.

We name an angle with letters. The vertex in the picture is the point O, so this is angle O. We can also use three letters: angle AOB or angle BOA. The letter of the vertex is always in the middle. In short we write ∠AOB.

Angles around us

Look around you: there are angles everywhere.

Can you find more angles in your room? Look at a door, a window, a chair and open scissors.

Right angle

The corner of a sheet of paper, of a book or of a window is a right angle.

A right angle is a square corner, like the corner of a square. We mark it with a small square instead of an arc.

A right angle is still a right angle when you turn it. All three angles in the picture are right angles.

Make a right-angle checker

You can make a right angle from any piece of paper, even a torn one.

Fold the paper in two. The fold is a straight line.
Fold it again so that the first fold lies exactly on top of itself.
The corner where the two folds meet is a right angle. This is your right-angle checker.

Now check an angle. Put the corner of the checker on the vertex and one edge of the checker along one side of the angle. Then look at the other side of the angle:

it is under the paper: the angle is smaller than a right angle;
it lies along the edge of the paper: the angle is a right angle;
it is outside the paper: the angle is bigger than a right angle.

At school you can check angles the same way with the square corner of a set square (a triangle ruler). In the angle maker at the top of this page, press Right-angle checker.

Acute angle

An acute angle is smaller than a right angle.

An acute angle is sharp, like the tip of a slice of pizza or the tip of a pencil.

Obtuse angle

An obtuse angle is bigger than a right angle, but its sides do not make a straight line.

An obtuse angle opens wide, like an open laptop.

Straight angle

When the two sides of an angle make one straight line, the angle is a straight angle.

Put your right-angle checker on the vertex of a straight angle: it covers exactly half of it. So a straight angle is as big as two right angles.

The four kinds of angles

Angle	Name	How big is it?
	acute angle	smaller than a right angle
	right angle	a square corner
	obtuse angle	bigger than a right angle, smaller than a straight angle
	straight angle	its sides make a straight line; it is as big as two right angles

Which angle is bigger?

How big an angle is depends only on how wide its sides open. The length of the sides does not matter.

Angle 1 has longer sides, but angle 2 is bigger: it opens wider.

To compare two angles, trace one of them on thin paper and put it on the other: vertex on vertex and side on side. The angle that fits inside the other one is the smaller angle.

Longer sides do not make an angle bigger. If you draw the sides longer (the dashed lines), the angle stays the same.

Angles in shapes

At every corner of a shape two sides meet and make an angle. Count the corners and you know how many angles the shape has.

A triangle has 3 sides and 3 angles.
A square and a rectangle have 4 angles each, and all four are right angles.
The house shape has 5 angles: 3 right angles and 2 obtuse angles.
A circle has no straight sides, so it has no angles.

Angles on a clock

The hands of a clock make an angle. Its vertex is the middle of the clock. At 1:00, 2:00, 3:00 and so on, the long hand points at 12 and the short hand points at the hour.

At 3:00 the hands make a right angle, and at 6:00 a straight angle. At 1:00 the angle is acute, and at 5:00 it is obtuse.

Turns

An angle also shows how far something turns. When the long hand goes from 12 to 3, it makes a quarter turn: it turns through a right angle. From 12 to 6 it makes a half turn: a straight angle, as big as two right angles. From 12 all the way round to 12 again it makes a full turn: four right angles.

Measuring angles in degrees

In grade 4 we also measure how big an angle is. The unit is the degree, and we write it with a small circle: 1°. A full turn is 360°.

Angle	Size
right angle	90°
straight angle (two right angles)	180°
full turn (four right angles)	360°

An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is more than 90° and less than 180°. A straight angle is 180°.

In the angle maker at the top of this page you can see the size of the angle in degrees.

How to use a protractor

We measure angles with a protractor.

Put the centre of the protractor on the vertex O.
Turn the protractor so that its zero line lies on one side of the angle, OA.
Find the 0 on the side OA and follow its row of numbers to the other side, OB. Read the number there: 50. So ∠AOB = 50°.

A protractor has two rows of numbers. Use the row that starts at 0 on the side OA. Check your answer: this angle is acute, so it must be less than 90°. It is 50°, not 130°.

Practice

Which angle is it?

Look at the angle and press its name. Not sure? Imagine the right-angle checker on the vertex.

Questions

1. How many angles does a triangle have? And a square?

A triangle has 3 angles. A square has 4 angles, and all of them are right angles.

2. What kind of angle do the hands of a clock make at 9:00?

A right angle: the long hand points at 12 and the short hand at 9.

3. What kind of angle do the hands of a clock make at 2:00? And at 4:00?

At 2:00 the angle is acute, and at 4:00 it is obtuse.

4. Mia says: "My angle has longer sides, so it is bigger." Is she right?

No. How big an angle is depends only on how wide its sides open, not on how long they are.

5. How many right angles make a straight angle? How many make a full turn?

Two right angles make a straight angle. Four right angles make a full turn.

6. Name three things in your classroom that have a right angle.

For example: the corners of a desk, of a book, of the board, of a door and of a window.

7. An angle is 35°. What kind of angle is it?

An acute angle, because 35° is less than 90°.

8. An angle is 120°. What kind of angle is it?

An obtuse angle, because 120° is more than 90° and less than 180°.

9. How many degrees are two right angles?

90° + 90° = 180°. Two right angles make a straight angle.