Home

Maths

Lines and angles

Angle rules

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Labib

Summary

Angle rules

In a nutshell

There are four rules you have to know about angles. You can apply these rules to solve problems involving missing angles.

The four angle rules

Here are the four rules you need to know.

RULE	DIAGRAM
Angles in a triangle add up to $180\degree$	$\alpha+\beta+\gamma=180\degree$
Angles on a straight line add up to $180\degree$	$A+B=180\degree$
Angles in a quadrilateral add up to $360\degree$	$\alpha+\beta+\gamma+\delta=360\degree$
Angles around a point add up to $360\degree$	$\alpha+\beta+\gamma+\delta=360\degree$

Note: A quadrilateral is another name for a shape with 4 sides.

Missing angle problems

To solve problems involving missing angles, look at the question and see which rule applies to it. You may have to label unknown angles with $x$ and use algebra to solve for them.

Example

In the triangle below, the value of $\beta$ is $60\degree$ . The angle $\gamma$ is $20\degree$ more than the angle $\alpha$ . What is the size of the angle $\alpha$ ?

Maths; Lines and angles; KS3 Year 7; Angle rules

This question concerns angles in a triangle, so use the fact that the angles in a triangle add up to $180\degree$ .

$\alpha+\beta+\gamma=180$

$\alpha+60+\gamma=180$

$\alpha+\gamma=120$

The question also says that the angle $\gamma$ is $20\degree$ more than the angle $\alpha$ . Algebraically, this means that:

$\gamma=20+\alpha$

Use this new information together with the first equation to solve for $\alpha$ :

$\alpha+\gamma=120$

$\alpha+(20+\alpha)=120$

$2\alpha+20=120$

$2\alpha=100$

$\alpha=50$

The size of the angle $\alpha$ is $\underline{50\degree}$ .

Learn with Basics

Length:

Unit 1

Measuring angles in degrees

Unit 2

Angles around a point and on a straight line

Jump Ahead

Optional

Unit 3

Angle rules

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you solve problems involving missing angles?

First, identify which of the 4 rules applies to the question. Then, use algebra to find the missing angle by using the rule to create an equation.

What are the rules for angles in a triangle and angles in a quadrilateral?

Angles in a triangle add up to 180 degrees, and angles in a quadrilateral add up to 360 degrees.

What are the rules for the angles on a line and angles around a point?

Angles on a line add up to 180 degrees, and angles around a point add up to 360 degrees.

Home

Maths

Lines and angles

Angle rules

Videos

Summary

Exercises

Select Lesson

Statistics

Qualitative and quantitative data

Representing data: Graphs and charts

Mean, median, mode and range

Frequency tables

Averages from frequency tables

Averages from grouped frequency tables

Scatter graphs

Probability

Calculating probability

Equal and unequal probabilities

Relative frequency

Listing outcomes

Venn diagrams

Trigonometry

Pythagoras’ theorem

Trigonometric ratios: SOH CAH TOA

Finding missing lengths in a triangle

Finding missing angles in a triangle

Drawing shapes

Transformations

Constructions

Constructing triangles

Lines and angles

Types of angles

Angle rules

Interior and exterior angles

Parallel lines

Measures

Area and perimeter: Triangles and quadrilaterals

Area of compound shapes

Volume of prisms

Properties of shapes

Symmetrical shapes and rotational symmetry

Congruent shapes

Similar shapes

Nets and surface area

Shapes

Quadrilaterals: Types and properties

Triangles and regular polygons: Types and properties

Circles: Area and circumference

3D shapes: Identification and properties

Rates of change

Percentage change

Conversion factors

Imperial units

Solving best buy problems

Reading timetables

Maps and scale drawings

Speed: Formula and units

Density: Formula and units

Proportion

Ratio

Other graphs

Interpreting graphs

Solving simultaneous equations using graphs

Quadratic graphs

Travel graphs: Distance-time graphs

Conversion graphs

Straight line graphs

X and Y coordinates

Straight line graphs

Drawing straight line graphs

Finding the gradient

Equation of a straight line: y = mx + c

Drawing a graph of a linear equation

Estimating values using linear graphs

Formulae and equations

Substituting numbers into an expression

Writing and using formulae

Solving equations

Rearranging formulae

Number patterns and sequences

The nth term

Inequalities: Greater than or less than

Simultaneous equations

Algebraic manipulation

Algebraic notation

Algebraic terms

Simplifying algebraic expressions

Multiplying and dividing algebraic expressions

Single brackets: Expanding and factorising

Expanding double brackets: FOIL and multiplication grid

Fractions, decimals and percentages

Converting between fractions, decimals and percentages

Fractions

Fraction operations: Add, subtract, multiply, divide

Percentages

Rounding: Decimal places and significant figures

Rounding errors and estimating

Number calculations

Ordering numbers: Whole numbers and decimals

Addition and subtraction using the column method

Multiplying and dividing by powers of 10

Adding and subtracting decimals

Methods for multiplication and division

Order of operations: BIDMAS

Types of numbers

Understanding place value

Negative numbers: Add, subtract, multiply, divide

Special types of numbers

Multiples, factors and prime factors

Lowest common multiple and highest common factor

Square roots and cube roots

Writing indices and index laws

Standard form

Explainer Video

Tutor: Labib

Summary

Angle rules

In a nutshell

There are four rules you have to know about angles. You can apply these rules to solve problems involving missing angles.

The four angle rules

Here are the four rules you need to know.

RULE	DIAGRAM
Angles in a triangle add up to $180\degree$	$\alpha+\beta+\gamma=180\degree$
Angles on a straight line add up to $180\degree$	$A+B=180\degree$
Angles in a quadrilateral add up to $360\degree$	$\alpha+\beta+\gamma+\delta=360\degree$
Angles around a point add up to $360\degree$	$\alpha+\beta+\gamma+\delta=360\degree$

Note: A quadrilateral is another name for a shape with 4 sides.

Missing angle problems

To solve problems involving missing angles, look at the question and see which rule applies to it. You may have to label unknown angles with $x$ and use algebra to solve for them.

Example

In the triangle below, the value of $\beta$ is $60\degree$ . The angle $\gamma$ is $20\degree$ more than the angle $\alpha$ . What is the size of the angle $\alpha$ ?

This question concerns angles in a triangle, so use the fact that the angles in a triangle add up to $180\degree$ .

$\alpha+\beta+\gamma=180$

$\alpha+60+\gamma=180$

$\alpha+\gamma=120$

The question also says that the angle $\gamma$ is $20\degree$ more than the angle $\alpha$ . Algebraically, this means that:

$\gamma=20+\alpha$

Use this new information together with the first equation to solve for $\alpha$ :

$\alpha+\gamma=120$

$\alpha+(20+\alpha)=120$

$2\alpha+20=120$

$2\alpha=100$

$\alpha=50$

The size of the angle $\alpha$ is $\underline{50\degree}$ .

Learn with Basics

Length:

Unit 1

Measuring angles in degrees

Unit 2

Angles around a point and on a straight line

Jump Ahead

Optional

Unit 3

Angle rules

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you solve problems involving missing angles?

First, identify which of the 4 rules applies to the question. Then, use algebra to find the missing angle by using the rule to create an equation.

What are the rules for angles in a triangle and angles in a quadrilateral?

Angles in a triangle add up to 180 degrees, and angles in a quadrilateral add up to 360 degrees.

What are the rules for the angles on a line and angles around a point?

Angles on a line add up to 180 degrees, and angles around a point add up to 360 degrees.