angles problem solving ks3

Missing Angles

Related worksheets.

Find the missing angles in a triangle, around a point, in a quadrilateral, find opposite and supplementary angles, or find angles which require multi-step problem solving skills.

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Game Objectives

New Maths Curriculum:

Year 3: Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle

Year 4: Identify acute and obtuse angles and compare and order angles up to two right angles by size

Year 5: Identify: multiples of 90°, angles at a point on a straight line and ½ a turn (total 180°); angles at a point and one whole turn (total 360°); reflex angles; and compare different angles

Year 6: Find unknown angles where they meet at a point, are on a straight line, and are vertically opposite

Angle Rules

Angles on a straight line

• Angles at a point on one side of a straight line add up to 180°.

Angles around a point

• Angles around a point add up to 360°.

1.1 Place Value

1.1.1 Ordering Numbers

1.1.2 Comparing Numbers

1.1.3 Equals Symbols

1.1.4 Adding Negative Numbers

1.1.5 Subtracting Negative Numbers

1.1.6 Multiplying Negative Numbers

1.1.7 Dividing Negative Numbers

1.1.8 End of Topic Test - Place Value

1.2 Factors & Multiples

1.2.1 Factors

1.2.2 Prime Numbers

1.2.3 Multiples

1.2.4 Prime Factors

1.2.5 Highest Common Factors

1.2.6 Highest Common Factor Prime Factors

1.2.7 Lowest Common Multiples

1.2.8 Lowest Common Multiples Prime Factors

1.2.9 End of Topic Test - Factors & Multiples

1.3 Operations

1.3.1 Addition

1.3.2 Subtraction

1.3.3 Multiplication 10,100...

1.3.4 Grid Multiplication

1.3.5 Division by 10s

1.3.6 Powers

1.3.7 Roots

1.3.8 Surds

1.3.9 Rationalise denominator

1.3.10 Simplify Surds

1.3.11 BIDMAS

1.3.12 Inverse Ops

1.3.13 Standard Form

1.3.14 Addition in Standard Form

1.3.15 Subtraction in Standard Form

1.3.16 End of Topic Test - Standard Form

1.4 Fractions, Decimals & Percentages

1.4.1 Fractions

1.4.2 Mixed & Improper Fractions

1.4.3 Write 2 Numbers as Fractions

1.4.4 Adding Fractions

1.4.5 Subtracting Fractions

1.4.6 Multiplying Fractions

1.4.7 Dividing Fractions

1.4.8 Finding Fractions

1.4.9 Improper & Mixed Fractions

1.4.10 Decimal Place Value

1.4.11 Fraction to Decimal

1.4.12 Find Percentage Unitary

1.4.13 Fraction to Percentage

1.4.14 Percentage to Fraction

1.4.15 Percentage to Decimal

1.4.16 Decimal to Percentage

1.4.17 Percentage using Decimal

1.4.18 End of Topic Test - Fractions

1.5 Growth & Decay

1.5.1 Population Growth

1.5.2 Compound Growth & Decay

1.5.3 Compound Interest

1.5.4 Compund Interest 2

1.5.5 Depreciation

1.6 Measurements & Units

1.6.1 Standard Units 1

1.6.2 Standard Units 2

1.6.3 Standard Units 3

1.6.4 Length

1.6.6 Volume

1.6.7 Capacity

1.6.9 Money

1.6.10 Mass

1.7 Accuracy

1.7.1 Decimal Rounding

1.7.2 SigFig Rounding

1.7.3 Estimations

1.7.4 Upper Lower Bounds

2.1 Introduction to Algebra

2.1.1 Algebra Basics

2.1.2 Algebraic Concepts

2.1.3 Writing Expressions

2.1.4 Collecting Terms

2.1.5 Common Factors

2.1.6 Expanding Brackets

2.1.8 Rearranging Formulae

2.1.9 End of Topic Test - Introduction to Algebra

2.2.1 Coordinates

2.2.2 Gradient and Intercept

2.2.3 Calculate Gradient &Y-intercept

2.2.4 Finding Equation

2.2.5 Quadratic Graphs

2.3 Solving Equations

2.3.1 Solve Linear Equations

2.3.2 Words To Equation

2.3.3 Solve Linear Equations Graphically

2.3.4 Solve Inequality

2.3.5 Graphing Inequalities

2.3.6 End of Topic Test - Graphs & Equations

2.3.7 Simultaneous Equations

2.3.8 Simultaneous Equations Graph

2.3.9 Quadratic +/-

2.3.10 Factorise Quadratics

2.3.11 Complete the Square

2.4 Sequences

2.4.1 Arith & Geo Sequences

2.4.2 Key Sequences

2.4.3 Nth Term Rules

2.4.4 Find NthTerm in Linear Sequence

2.4.5 End of Topic Test - Sequences

2.4.6 Find Nth Term in Quadratic Sequence

3 Ratio, Proportion & Rates of Change

3.1 Manipulating Ratios

3.1.1 Manipulating Ratios

3.1.2 Turn Ratios into Equations

3.1.3 Part:Part Ratio

3.1.4 Part:Whole Ratio

3.1.5 Differences in Ratios

3.1.6 Fractions in Ratios

3.1.7 Ratios to Fractions

3.2 Ratios in Practice

3.2.1 Covert Units

3.2.2 Formula Triangles

3.2.3 Scale Factors

3.2.4 End of Topic Test - Ratios

3.2.5 Ratios in Shapes

3.3 Percentage & Finance

3.3.1 Percentage Increase/Decrease

3.3.2 Percentage Change

3.3.3 Original Value

3.3.4 Profit, Interest & Discount

3.3.5 Simple Interest

3.4 Proportion

3.4.1 Proportion

3.4.2 Direct Proportion

3.4.3 Inverse Proportion

3.4.4 End of Topic Test - Percentages & Proportion

4 Geometry & Measures

4.1 Introduction to Geometry

4.1.1 LinesAngles1

4.1.2 LinesAngles2

4.1.3 Regular Polygons

4.1.4 Triangles and Angles

4.1.5 Quadrilaterals

4.1.6 Midpoints

4.1.7 Bisectors and Perpendiculars

4.1.8 Angle Rules

4.1.9 Angles in Parallel Lines

4.1.10 Angles in a Polygon

4.1.11 Angles in a Triangle

4.1.12 Bearings

4.1.13 End of Topic Test - Geometry

4.2 Ruler & Compass Constructions

4.2.1 Midpoint

4.2.2 Bisectors and Perpendiculars

4.3 Perimeter & Area

4.3.1 Perimeter

4.4 Triangles, Quadrilaterals & Circles

4.4.1 Types of Triangle

4.4.2 Angles & Triangles

4.4.3 Congruence

4.4.4 Congruent Triangles

4.4.5 Similar Triangles

4.4.6 Scale Factors & Enlargement

4.4.7 Properties of Circle 1

4.4.8 Properties of a Circle 2

4.4.9 Area of a Circle

4.4.10 Circumference of a Circle

4.5 Transformations

4.5.1 Types of Transformations

4.5.2 Effects of Transformations

4.6 Triangle Formulae

4.6.1 Pythagoras' Theorem

4.6.2 Trigonometric Ratios

4.7 3D Shapes

4.7.1 Types of 3D Shape

4.7.2 Plans & Elevations

4.7.4 Volume of 3D Shapes

4.7.5 Volume of a Cuboid

4.7.6 Volume of a Cylinder

4.7.7 Volume of a Sphere

4.7.8 Volume of a Hemisphere

4.7.9 Volume of a Cone

4.7.10 Volume of a Pyramid

4.7.11 Surface Area of a Cuboid

4.7.12 Surface Area of a Cylinder

4.7.13 Surface Area of a Sphere/Hemisphere

4.7.14 Surface Area of a Cone

4.7.15 Surface Area of Composite Shapes

4.7.16 End of Topic Test - Triangles, Area, & 3D Shapes

4.8 Vectors

4.8.1 Vector Introduction

4.8.2 Vectors

5 Probability

5.1 Introduction to Probability

5.1.1 Probability

5.1.2 Probability scale

5.1.3 Randomness & Fairness

5.1.4 Sum of Probabilities

5.1.5 Relative & Expected Frequency

5.1.6 Frequency Tables

5.1.7 Use Frequency Trees

5.1.8 Complete Frequency Trees

5.2 Representing Probability

5.2.1 Sample Space Diagrams

5.2.3 Venn Diagrams

5.3 Probability Calculations

5.3.1 Theoretical Probability

5.3.2 Venn Diagram Probabilities

5.3.3 Multiple Events

5.3.4 Dependent & Independent Events

5.3.5 Calculating Probabilities

5.3.6 Complex Tree Diagrams

5.3.7 End of Topic Test - Probability

6 Statistics

6.1 Introduction to Statistics

6.1.1 Statistics Basics

6.1.2 Statistics Basics 2

6.1.3 Comparing Data

6.1.4 Comparing Datasets

6.1.5 Writing Comparisons

6.1.6 Frequency Table

6.2 Charts & Graphs

6.2.1 Bar Charts

6.2.2 Pie Charts

6.2.3 Pictograms

6.2.4 Scatter Graphs

6.2.5 Making Predictions

6.2.6 Correlation and Causation

6.2.7 Outliers

6.2.8 End of Topic Test - Statistics

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Bisectors and Perpendiculars

Angles in Parallel Lines

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Mastery - angles

Five simple worksheets on angles for KS3. Each PowerPoint worksheet follows the same layout and includes similar sections for fluency, misconception, reasoning, problem-solving and application. Skills covered:

• angles on a straight line and at a point
• angles in triangles
• angles in quadrilaterals
• angles on parallel lines

The worksheets could be used during topic teaching on angles, as starters, plenaries or for diagnosing misconceptions or could be used during the year to aid recall.

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Lesson details

Key learning points.

• Sometimes there can be more than one valid approach to a problem.
• You should consider all the skills you have.
• Consider multiple approaches and take time to evaluate each.
• Keep the goal in mind throughout, remember what you are trying to find out.

Common misconception

Pupils may struggle to identify a right-angled triangle in the problem.

Encourage pupils to sketch the question out and add any known right angles or perpendicular lines, as this may lead to a right-angled triangle.

Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

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KS3 Angle pile up problems, 25 questions, Angles in a quadrilateral, triangle

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

27 November 2022

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• Two problems are included
• First problem is repeated 3 times on one sheet for ease of printing
• Second problem is repeated twice to optimise printing
• First problem regards solely angles within a triangle.
• Second problem regards angles within a triangle, quadrilateral and the harder sheet 2 includes alternate angles (the lattter doesn’t have to be included).
• Cheat sheet, which is a good structure for supporting any ability to complete at least the first task.

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