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KS2

Drawing and measuring angles

Part of MathsLines and anglesYear 6

What is an angle?

Rohan holding a protractor

An angle is the amount of turn between two lines. An angle is measured in degrees (°).

Angles are a way of describing the space between 2 lines that begin at the same point. They are a measure of how much you have to turn one of the lines so that it sits on top of the other.

There are 360° in a full circle and an angle can be measured anywhere from 0° to 360°.

Rohan holding a protractor

Quiz: Drawing and calculating angles

Why not see how much you know about this topic already? Then work through the page and see if you can beat your score.

Types of angles

There are different types of angles based on their measurement.

Let's look at the different types.

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Right angle
A right angle looks like the corner of a square or the edge of a book. It is a perfect 90°, which is often shown by a small square drawn in between the two lines
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Acute
An acute angle is an angles that is less than 90°. This makes them smaller than a right angle.
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Obtuse
An obtuse angle is an angle that is bigger than 90° degrees, but doesn’t reach a straight line at 180°.
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Straight line
A straight line is 180˚
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Reflex
A reflex angle is an angle that is greater than 180°.

Using a protractor

You can use a protractor to measure and draw angles. It has a clockwise and an anti-clockwise scale.

This is so that you can measure angles to the left or right.

A protractor

Let's have a go at using a protractor to measure some angles.

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What could this angle be? It's a good idea to estimate the angle first and then measure it. You can see it's an acute angle, so it's less than 90°.
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Find the base line on the protractor (it's marked 0° at one end and 180° at the other end). Place the middle of the base line exactly at the point of the angle. Make sure that one of the angle lines goes through the zero.
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Look to see where the other line meets the scale around the edge of the protractor. Here the inner scale shows the size of the angle. This angle measures 65°.
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Let's look at another. Look at this angle. Can you see that this time it's an obtuse angle?
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Look for the zero line that the base angle goes through. It's on the inside, so you must read the inside numbers. The other angle line is between 130° and 140°. So the angle 135°.

Useful equipment

If you know how to measure angles, you can use a similar method to help you draw angles.

You will need:

A pencil, protractor and ruler.

Drawing angles

Now let's try drawing an angle.

Let's use a protractor to draw an angle of 50°.

Before starting, can you picture what you think the angle will look like and sketch it?

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Step 1: Draw a single base line with a ruler.
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Step 2: Place the centre of the protractor at one end of the line. This will become the vertex (corner) of the angle. Make sure the line runs along the base line of the protractor.
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Step 3:  Look for 50° on the protractor. There are inside and outside numbers on the protractor. Look for the zero that is on the same side as the line. It is on the left-hand side and on the outside. Make a mark where the 50° is on the outside scale.
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Step 4: Remove the protractor. Using a ruler, the mark you made to the end of the line that was in the centre of the protractor.

Calculating angles

, angles are measured in degrees (°) and there are 360° in a full turn.

One half turn is 180°, which is a straight line.

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Angles on a straight line add up to 180°. Therefore, a + b = 180°
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If the straight line is divided into two angles, and we know one of the angles, we can work out the other. 120° + b = 180°
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Can you work out angle b? 120° + b = 180°. Therefore, b = 180° − 115°, which is = 60°
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If the straight line is divided into three angles, all three angles add up to 180°.

Example 1

Can you work out what angle b is?

Example 2

Vertically opposite angles are the angles directly opposite each other when a straight line crosses over another straight line.

They are always equal.

2 vertically opposite angles where a straight line crosses over another straight line. Angle A has angles b, c and d. One angle is 70°. Angle B has an angle at 145° and angles b, c and d.

Can you work out angle c is in these diagrams?

Example 3

Angles at a point add up to 360°.

What is the value of angle A?

Example 4

What is the value of angle B?

More on Lines and angles

Find out more by working through a topic

Angles in polygons
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Horizontal and vertical lines
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Parallel and perpendicular lines
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What is an angle?
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