# Angles

## Home learning focus

Learn about different triangles and quadrilaterals and their properties.

This lesson includes:

- one video
- learning summary
- one activity sheet

# Learn

Students looking to achieve grade 4 in GCSE Maths must understand that the angles in a triangle add up to **180°** and in quadrilaterals add up to **360°**.

Check your understanding of the angles in a triangle by watching this short video from BBC Bitesize, GCSE Maths.

Read pages 4 and 5 of our 'Angles, lines and polygons' Bitesize revision guide to understand:

## Triangles

**Types of triangle**

A triangle is a 2D shape with **three sides**. A 2D (two -dimensional) shape is has two dimensions, usually length or height and width.

There are four different triangles with different properties.

A **scalene** triangle has **three** sides of different lengths and three unequal angles.

An **isosceles** triangle has **two** sides of equal length. The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.

An **equilateral** triangle has **three** sides of equal length. The dashes on the lines show they are equal in length. All of the angles are also equal.

A **right-angled** triangle is a triangle that has a right angle.

## Interior and exterior angles

The angles inside a shape are called **interior angles**.

If the side of a triangle is extended, the angle formed outside the triangle is the **exterior angle**.

The interior angle and its corresponding exterior angle **always** add up to **180°**.

In this image, g is the interior angle and h is the exterior angle, so, g + h = 180°.

## The sum of interior angles in a triangle

To prove a + b + c = 180°, firstly draw a line parallel to one side of the triangle.

d = b (alternate angles are equal)

e = c (alternate angles are equal)

a + d + e = 180° (angles on a straight line add up to 180°)

So a + b + c = 180°.

## Quadrilaterals

A quadrilateral is a 2D shape with four sides. There are six special quadrilaterals with different properties.

**Types of quadrilateral**

**Square**

- A square has four sides of equal length.
- It has four right angles (90°).
- The opposite sides are parallel.
- The diagonals
**bisect**(divide into two equal sections) each other at right angles.

**Rectangle**

- A rectangle has two pairs of equal sides.
- It has four right angles (90°).
- The opposite sides are parallel.
- The diagonals bisect each other.

**Parallelogram**

- A parallelogram has two pairs of equal sides.
- It has two pairs of equal angles.
- The opposite sides are parallel.
- The diagonals bisect each other.

**Rhombus**

- A rhombus has four sides of equal lengths.
- It has two pairs of equal angles.
- The opposite sides are parallel.
- The diagonals bisect each other at right angles.

**Trapezium**

- A trapezium has one pair of parallel sides.

**Kite**

- A kite has two pairs of equal sides.
- It has one pair of equal angles.
- The diagonals bisect at right angles.

## The sum of the interior angles in a quadrilateral

The sum of all the interior angles in a quadrilateral is 360°.

This fact and the properties of quadrilaterals can be used to calculate angles.

**Example**

Find angle d:

d = 360 - 100 - 70 - 30 = 160°

To learn more about angles look at the Angles, lines and polygons Bitesize guide here.

# Practise

## Activity 1

**Angles**

Complete the activity sheet from Beyond on angles in a triangle to test your knowledge. You can print it out or write your answer on a piece of paper.

# Choose your exam specification

BBC Bitesize has GCSE exam board-relevant content for students in England, Northern Ireland and Wales. Chose the exam specification that matches the one you study.

# There's more to learn

Have a look at these other resources around the BBC and the web.