# Angles

## Home learning focus

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°.

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

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°

# 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.