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Triangle Exterior Angle Theorem Practice Worksheet | Multi-Step Equations

Triangle Exterior Angle Theorem Practice Worksheet | Multi-Step Equations

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

24 July 2026

pdf, 232.5 KB
pdf, 232.5 KB

A worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem. Detailed solutions are included.

Master the exterior angle theorem of triangles alongside algebraic equations. This no-prep, 12-question worksheet challenges Key Stage 3 and Key Stage 4 students to apply geometric properties to set up and solve multi-step linear equations. Fully worked, step-by-step solutions are included. Ideal for independent practice, homework, revision, or cover work.

Looking for a rigorous, ready-to-print activity to strengthen your students’ understanding of the exterior angle theorem?
This 12-question practice worksheet is carefully scaffolded to guide students from foundational geometric facts into multi-step algebraic mastery. Rather than simply calculating missing angles, students are required to apply angle properties to formulate and solve linear equations.

What is Included in This Resource?
• 12 Scaffolded Questions: The exercises transition smoothly in difficulty to build student confidence.
• Questions 1 to 5: Finding unknown interior or exterior angles using straightforward addition and subtraction.
• Questions 6 to 8: Multistep geometry questions incorporating properties of isosceles triangles, supplementary angles, and linear pairs.
• Questions 9 to 12: Advanced algebraic integration where students form equations from the diagram and solve for x (e.g. 23x = 66 + 12x).
• Complete Step-by-Step Solutions: A fully worked answer key is provided to make self-assessment or teacher grading fast and easy.

Why Teachers Value This Resource:
• Zero Preparation Required: Simply download, print, and distribute to your class.
• Versatile Classroom Use: Perfect for standard classwork, homework tasks, targeted revision sessions, or structured cover lessons.
• Combines Geometry and Algebra: An excellent way to reinforce linear equation-solving skills within a shape-based module.

Target Curriculum & Year Groups:
• UK Curriculum: Key Stage 3 and Higher/Foundation GCSE Key Stage 4 (Geometry and Measures / Algebra strands).
• Recommended Classes: Year 8, Year 9, and Year 10 math sets.

Get this resource as part of a bundle and save up to 42%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Geometry Triangle Congruence & Angle Relationships Worksheets Bundle

A collection of 7 worksheets on the following topics: * Types of Triangles. A worksheet on determining the type of a given triangle with respect to its interior angles (acute-angled, obtuse-angled, right-angled) and with respect to its sides (scalene, isosceles, equilateral). * Triangle Angle Sum Theorem. A worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem. * Exterior Angle Theorem. A worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem. * Isosceles, Equilateral and Right-Angled Triangles. A worksheet on isosceles, equilateral and right-angled triangles and the angle properties of these triangles. Congruent Triangles Introduction. An introductory worksheet on congruent triangles. The exercises require to identify the corresponding equal angles or sides of some given congruent triangles. * Congruent Triangles (SSS, SAS, ASA, AAS). A worksheet on determining whether triangles are congruent by Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). * Congruent right-angled triangles. A worksheet on deciding whether a given pair of right-angled triangles are congruent. Detailed solutions are included. Looking for a comprehensive, no-prep collection of resources to help your secondary students master triangle properties, angle rules, and geometric proofs? This ultimate 7-lesson worksheet bundle provides a complete practice path, taking students from basic triangle classifications all the way to rigorous, multi-step congruence proofs! Whether your classes are calculating missing values with algebraic equations or practicing formal proofs using SSS, SAS, ASA, and AAS, this resource has everything you need. Best of all, complete, step-by-step solutions are included for every problem to save you hours of marking time or to allow for easy student self-assessment! **What’s Included in This Bundle?** This package features 7 carefully structured resource packets (complete with full solutions) that scaffold student learning: * **Resource 1: Types of Triangles** – Focuses on classifying triangles by their interior angles (acute-angled, obtuse-angled, right-angled) and side lengths (scalene, isosceles, equilateral) using numeric values and side markings. * **Resource 2: Triangle Angle Sum Theorem** – Multi-level practice for finding the missing variable x inside a triangle. Problems range from basic arithmetic to advanced multi-step algebraic equations and vertically opposite angle setups. * **Resource 3: Exterior Angle Theorem** – Students apply the exterior angle theorem to solve for x using single values, linear equations, and supplementary angle properties. * **Resource 4: Isosceles, Equilateral & Right-Angled Triangles** – Deepens conceptual understanding of special triangle properties, base angle rules, and solving for missing values in isosceles right triangles. * **Resource 5: Introduction to Congruent Triangles** – Students practice identifying corresponding equal sides and angles across matching congruent shapes. * Resource 6: Congruence Concept Check**** – A rigorous True or False section testing deep conceptual knowledge of rigid transformations (rotations) and triangle types. * **Resource 7: Comprehensive Geometry Proofs** – 11 distinct, diagram-based proofs where students analyse given markings, identify shared common sides, midpoints, heights, angle bisectors, and formally prove congruence using SSS, SAS, ASA, and AAS rules. **Why Teachers Love This Resource:** * **Ready to Print:** Just download, photocopy, and you are ready to teach! * **Step-by-Step Answer Keys:** Full calculations, geometric reasoning diagrams, and complete criteria listings are provided for every problem, making marking or peer-assessment a breeze. * **Scaffolded Practice:** Tasks build naturally from simple classification and value calculations to abstract, higher-level diagram analysis and formal proofs. * **Versatile Classroom Use:** Perfect for main lesson tasks, independent classwork, homework assignments, cover work, or revision. **Skills Covered:** * Classifying triangles by side lengths and interior angles. * Applying the Triangle Angle Sum and Exterior Angle rules algebraically. * Working with geometric diagram properties: shared common sides, vertically opposite angles, midpoints, and angle bisectors. * Proving triangle congruence using SSS, SAS, ASA, and AAS criteria. * Verifying theorems regarding isosceles and equilateral triangle properties. **Curriculum & Key Stage Alignment:** * **Key Stages:** Key Stage 3 (KS3) Extension & Key Stage 4 (KS4) GCSE Maths * **Exam Board Suitability:** Ideal for Higher Tier GCSE (AQA, Edexcel, OCR) * **Topic:** Geometry and Measures -Congruence and Similarity -Geometric Proof & Angle Rules

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Three worksheets on the triangle angle theorem and triangle exterior angle theorem. The exercises require to find missing angles by using the two theorems. Detailed solutions are included. There is one worksheet on each theorem and one worksheet on both theorems. Save time and money with this complete 3-worksheet bundle tracking triangle angle theorems and algebra integration! Designed to take students from foundational geometry to advanced multi-step equations, this mini-unit includes separate worksheets for the Triangle Angle Sum Theorem, the Exterior Angle Theorem, and a comprehensive mixed revision sheet. All 36 questions feature complete, step-by-step solutions! ________________________________________ Looking for a complete, scaffolded resource bundle to help your students master interior and exterior triangle angles while reinforcing crucial algebraic skills? This 3-worksheet mini-unit bundle is the ultimate no-prep solution for your geometry module. It bridges the gap between simple geometric properties and multi-step algebraic equations, taking Key Stage 3 and Key Stage 4 students from basic calculations to complex geometric puzzles! **What is Included in This Money-Saving Bundle?** You get three distinct, 12-question worksheets (totaling 36 unique questions) that systematically increase in difficulty. • **Worksheet 1: Triangle Angle Sum Theorem** o Focuses on finding missing interior angles. o Progresses from basic integer calculations (including right-angled, isosceles, and equilateral triangles) to multi-step linear algebraic expressions with variables on both sides. o Introduces complex diagrams featuring vertically opposite angles. • **Worksheet 2: Exterior Angle Theorem** o Focuses on the relationship between exterior angles and remote interior angles. o Challenges students with straight-line supplementary linear pairs and multi-step algebraic integration (e.g. 6x + 20x + 4 = 160). • **Worksheet 3: Mixed Revision & Synthesis** o Seamlessly combines both theorems into a comprehensive check for understanding. o Features a balanced mix of scalene, right-angled, isosceles, and equilateral triangles so students must analyze geometric notation and markings to succeed. • **3 Complete Step-by-Step Solutions Keys:** Every single worksheet comes with fully worked answer keys, making grading effortless or allowing for perfect student self-assessment. **Why Teachers Value This Bundle:** • **Massive Time Saver:** Three full days of targeted practice, homework tasks, math centres, exam revision, or structured cover lessons, ready to download and print. • **Built-In Algebra Reinforcement:** Perfect for showing students how algebraic equation-solving skills are applied directly inside geometric shapes. • **Scaffolded Learning Track:** Great for differentiation, allowing you to meet students where they are and pull them forward into advanced multi-step logic. **Target Curriculum & Year Groups:** • **UK Curriculum:** Key Stage 3 and Higher/Foundation GCSE Key Stage 4 (Geometry and Measures / Algebra strands). • **Recommended Classes:** Year 8, Year 9, and Year 10 maths sets. ________________________________________

£3.50
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A collection of seven worksheets on the following topics: Classifying Triangles. There is a worksheet on classifying triangles by their sides, a worksheet on classifying triangles by their angles and a worksheet on classifying triangles by their sides and angles. The students are given some triangles to classify and in some cases they are required to find missing angles of the triangles (using the triangle angle sum theorem). In addition they are given some other exercises (true/false, blanks to complete) in order to test their knowledge on the different types of triangles. Triangle Angle Sum Theorem. There is a worksheet on the triangle angle sum theorem. The exercises require to find missing angles by using the triangle angle sum theorem and the properties of special types of triangles (isosceles and equilateral). Exterior Angle Theorem. There is a worksheet on the triangle exterior angle theorem. The exercises require to find missing angles by using the triangle exterior angle theorem. Triangle Angle Sum Theorem and Exterior Angle Theorem. There is a worksheet on the triangle angle theorem and triangle exterior angle theorem. The exercises require to find missing angles by using the two theorems. Parallel Lines Cut by A Transversal. There is a worksheet to help students strengthen their skills in the concept of parallel lines cut by a transversal. The following angle relationships occur in the exercises: complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, consecutive interior angles and corresponding angles. In the first two exercises, students are given a diagram with two parallel lines cut by a transversal and are required to identify the relationships between some given pairs of angles. In the next exercises, students are given some diagrams with missing angles which are required to find by using their knowledge on the topic. Elementary and harder exercises are included. Detailed solutions are included. Ready-to-print KS3 and GCSE Maths worksheets pack! Includes comprehensive practice pages and full step-by-step solutions for angles in parallel lines, triangle angle sums, and properties. ________________________________________ Master essential geometry concepts with this comprehensive, ready-to-print maths worksheets pack! Designed perfectly for Key Stage 3 (KS3) and GCSE foundation/higher tiers (Years 9, 10, and 11), this resource provides structured, scaffolded practice for students learning to identify angle facts and calculate missing measurements. Whether you need independent classwork, homework tasks, revision packs, or emergency cover lessons, these printable pages are completely ready to go. **What’s Included in This Pack?** • Angles in Parallel Lines: Practice identifying and using alternate, corresponding, co-interior (consecutive interior), vertically opposite, and supplementary angles. • Angles in Triangles: Missing angle calculations ranging from simple numeric problems to multi-step algebraic equations. • Exterior Angle Theorem: Targeted problems to help students master the rule that the exterior angle equals the sum of the two opposite interior angles. • Classifying Triangles: Sorting activities to identify triangles by their sides (scalene, isosceles, equilateral) and by their angles (acute, right-angled, obtuse). • Full Step-by-Step Solutions: Complete, detailed teacher answer sheets are included for every single problem to allow for quick marking or student self-assessment! **Curriculum Alignment** • KS3 National Curriculum: Apply conventional terms and notations for points, lines, parallel lines; derive and illustrate properties of triangles; use alternate and corresponding angles. • GCSE Maths (AQA, Edexcel, OCR): Standard geometry properties involving angles in parallel lines, triangles, and polygon angle facts.

£5.90

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