How many degrees are there in a full turn?

There are 360 degrees in a full turn.

What is a reflex angle?

A reflex angle is bigger than 180 degrees but less than 360 degrees.

How do I know which scale to read on a protractor?

Start at the 0 that lines up with one arm of the angle. Then check if the angle is acute or obtuse.

Is a rectangle a regular polygon?

No. A rectangle has equal angles but its sides are not all equal, unless it is a square.

Year 5 angles and polygons lesson to download as PDF

This Year 5 angles and polygons lesson is written for pupils aged 9-10 and follows the National Curriculum. In short, it shows you how to measure and draw angles, find missing angles at a point and on a line and tell regular from irregular polygons. Before you start, it helps to revise percentages and metric and imperial units, perimeter, area and volume, because this lesson builds on them.

Table of Contents

Year 5 angles and polygons lesson: what you will learn

Hello, I am Otto! An angle tells us how much something turns. We see angles in opening doors, the hands of a clock and the corners of buildings. Polygons are flat shapes with straight sides. In Year 5 you measure and compare angles in degrees, find missing angles on a straight line and around a point, and meet regular and irregular polygons.

Starter activity

Stand up and face the board. Turn a quarter of the way round to your right. You have turned through a right angle, which is 90 degrees. Turn another quarter turn. Now you have made a half turn, 180 degrees. Four quarter turns bring you back to the start, a full turn of 360 degrees. Use your body to check each fact as you read.

Measuring turns in degrees

Definition: angle and degree

An angle measures an amount of turn. We measure it in degrees, written with the symbol °. The two straight lines that form an angle are its arms, and the point where they meet is the vertex.

Key fact: turns

A full turn is 360°, a half turn is 180° and a quarter turn is 90°. A clock hand moves 30° each hour because 360 ÷ 12 = 30.

Types of angle

Definition: types of angle

An acute angle is less than 90°. A right angle is exactly 90°. An obtuse angle is between 90° and 180°. A straight angle is 180°. A reflex angle is between 180° and 360°.

Example 1

What type of angle is 135°? And 250°?

135° is more than 90° and less than 180°, so it is obtuse. 250° is more than 180° and less than 360°, so it is reflex.

Method: measuring an angle with a protractor

Place the centre of the protractor on the vertex of the angle.
Line up the 0° line with one arm of the angle.
Read the scale that starts at 0° on that arm.
Check your answer with an estimate: is the angle acute or obtuse? Does the number match?

Angles on a straight line and at a point

Rule: angles on a straight line

Angles on a straight line add up to 180°. If one angle is known, subtract it from 180° to find the other.

Example 2

Two angles lie on a straight line. One is 125°. Find the other angle, x.

Angles on a straight line add to 180°. x = 180° − 125° = 55°.

Rule: angles at a point

Angles around a point add up to 360°, a full turn. To find a missing angle, add the known angles and subtract the total from 360°.

Example 3

Three angles meet at a point: 110°, 150° and x. Find x.

110° + 150° = 260°. x = 360° − 260° = 100°.

Watch out

Do not mix up 180° and 360°. Straight line: 180°. Whole turn around a point: 360°. A quick way to remember is that a straight line is half of a turn.

Polygons

Definition: polygon

A polygon is a closed flat shape with straight sides. The corners are called vertices. Polygons are named by the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9) and decagon (10).

Definition: regular and irregular polygons

A regular polygon has all its sides the same length and all its angles equal. A polygon that is not regular is irregular. A square is a regular quadrilateral; a rectangle that is not a square is irregular.

These are a regular pentagon, a regular hexagon and a regular octagon.

Example 4

A regular hexagon has sides of 6 cm. What is its perimeter?

A hexagon has 6 sides, all equal because it is regular. Perimeter = 6 × 6 cm = 36 cm.

Key fact: triangles

An equilateral triangle has three equal sides. An isosceles triangle has two equal sides. A scalene triangle has no equal sides. A right-angled triangle has one angle of 90°.

Example 5

A regular polygon has a perimeter of 56 cm and each side is 7 cm long. How many sides does it have and what is it called?

56 ÷ 7 = 8, so it has 8 sides. A polygon with 8 sides is an octagon.

Did you know?

The word "polygon" comes from Greek words meaning "many angles". The Greek mathematician Euclid wrote a famous book about geometry over 2,300 years ago. The degree is probably based on the Babylonian idea of 360 parts in a circle, since 360 can be divided by so many numbers. Honeybees build their honeycomb out of regular hexagons because hexagons fit together without leaving any gaps.

Otto’s tip

Always make a quick estimate of an angle before you measure it. If the angle looks smaller than a corner of a book, it must be acute. If your protractor says 130° for that angle, you have read the wrong scale!

How to use this Year 5 angles and polygons lesson

First, read the key points so that you know where the Year 5 angles and polygons lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the angles and polygons worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the angles and polygons test and mark it with the test answers.

Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 5 angles and polygons lesson gives you everything you need for the chapter.