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Exterior Angle Theorem Worksheet with Answer Key | 8th Grade Math Geometry

Exterior Angle Theorem Worksheet with Answer Key | 8th Grade Math Geometry

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

11 August 2026

pdf, 135.24 KB
pdf, 135.24 KB

A worksheet on the exterior angles of a triangle. The exercises require to use the fact that an exterior angle of a triangle is equal to the sum of the two interior opposite angles. Solutions are included.

Master the exterior angle theorem and angles in triangles with this comprehensive, ready-to-print maths worksheet! Perfect for KS3, KS4, and GCSE Maths students, this resource includes fully worked step-by-step solutions to save you valuable marking time.

Help your secondary maths students master the geometric properties of triangles with this rigorous, no-prep practice worksheet! This resource is specifically designed to guide students from basic calculations using the exterior angle theorem to advanced multi-step problems involving special triangle properties.
Whether you need a quick homework assignment, a targeted revision lesson, a geometry cover lesson, or an in-class assessment, this printable activity provides clear, structured practice that aligns perfectly with secondary school maths curriculums.

What’s Included in This Resource?
• 6 Multi-Step Problems: Carefully sequenced questions covering interior angles, angles on a straight line, and exterior angles of triangles.
• Scaffolded Skill Building: Problems progress from basic application to challenging scenarios involving isosceles and equilateral triangles.
• Fully Worked Solutions: Step-by-step answers for every single problem to facilitate easy marking or student self-checking.

Skills Covered:
• Applying the exterior angle theorem to solve for unknown angles ((x)).
• Utilizing angles on a straight line and supplementary angles (adding up to 180 degrees).
• Using equilateral triangle properties to identify interior angle measures (60 degrees).
• Using isosceles triangle properties to determine equal base angles.
• Formulating and solving basic algebraic equations based on geometric diagrams.

Perfect For:
• Key Stage 3 (KS3) Math Classes (Years 7–9)
• Key Stage 4 (KS4) & GCSE Foundation and Higher Tiers
• Functional Skills Mathematics Level 2
• Homework, Classwork, Cover Work, or Exam Revision

Exam Board Alignment:
• Excellent preparation for Edexcel, AQA, OCR, and WJEC specifications covering properties of polygons, angles, and geometric reasoning.

Get this resource as part of a bundle and save up to 45%

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

Bundle

Angle Relationships, Parallel Lines & Triangles Geometry Bundle | GCSE 9-1

A collection of 6 worksheets on angles, lines and triangles based on the GCSE 9-1 specification. The following worksheets are included: * Types of angles * Complementary, supplementary and opposite angles * Angles in parallel lines * Sum of angles in a triangle * Exterior Angles of a Triangle * Isosceles, Equilateral and Right-Angled Triangles Detailed solutions are included. Master angle facts and triangle properties with this complete geometry worksheet bundle! Perfectly optimized for KS3 and GCSE 9-1 math revision (Foundation and Higher), this print-and-go pack covers parallel lines, angle types, and multi-step equations with full step-by-step worked solutions. ________________________________________ Looking for a rigorous, print-and-go resource to help your students master angle rules and geometric reasoning? This GCSE 9-1 Angles, Lines and Triangles Worksheet Bundle contains highly structured practice sheets designed to build fluency and algebraic confidence. Moving from basic angle classification to multi-step exam-style equations, this bundle is perfect for formal lessons, independent revision, homework packs, cover work, or intervention groups! Every page includes an uncrowded, student-friendly layout and comes paired with a complete, step-by-step worked solution key showing the exact algebraic workings to solve for \(x\). ________________________________________ **What's Included in This Bundle?** • **Types of Angles & Triangles:** Identification mastery for acute, obtuse, right, straight, and reflex angles, alongside scalene, isosceles, and equilateral properties. • **Complementary, Supplementary & Vertically Opposite Angles:** Multi-step algebraic equations requiring students to set up expressions that add up to 90 or 180 degrees. • **Angles in Parallel Lines:** Clear diagrams focusing on alternate, corresponding, and co-interior/allied angle theorems (using formal geometric reasons). • **Interior & Exterior Angles of Triangles:** Comprehensive practice applying the triangle angle sum theorem (180 degrees) and the exterior angle theorem. ________________________________________ **Perfect For:** • KS3 Maths: Building a strong foundational mastery of basic angle facts and algebraic manipulation. • KS4 / GCSE 9-1 Prep: targeted revision for both Foundation and Higher tier students aiming for maximum marks on geometry questions. • Cover Lessons & Homework: Structured, self-explanatory layout that requires zero preparation from you or a cover teacher. ________________________________________

£4.95
Bundle

Interior and Exterior Angles in Triangles & Polygons Geometry Worksheets

A collection of three worksheets on the following topics: * Sum of angles in a triangle: a worksheet on evaluating the third angle in a triangle given the other two using the fact that their sum is 180 degrees * Exterior Angles of a Triangle: a worksheet on the exterior angles of a triangle. The exercises require to use the fact that an exterior angle of a triangle is equal to the sum of the two interior opposite angles. * Interior and exterior angles in regular polygons: a worksheet on calculate the interior and exterior angle sum of regular polygons and the measure of each interior and each exterior angle of regular polygons. Detailed solutions are provided. Master interior and exterior angles with this comprehensive, ready-to-print geometry maths worksheet bundle! Perfect for KS3, KS4, and GCSE Maths classrooms, this 3-resource collection includes fully worked step-by-step solutions to save you valuable marking time. ________________________________________ Help your secondary maths students conquer geometric properties with this no-prep angles in triangles and polygons worksheet bundle! This collection features three carefully scaffolded, rigorous resources designed to take students from foundational angle rules to advanced multi-step geometric problem-solving. Whether you need targeted homework assignments, no-prep cover plans, extension tasks, or comprehensive exam revision, these printable activities provide clear, structured practice that fits seamlessly into any secondary school maths curriculum. **What’s Included in This Bundle?** This cost-saving bundle contains three complete worksheets, each including its own detailed, step-by-step fully worked solutions: **1. Sum of Angles in a Triangle Worksheet** o 10 multi-step problems calculating missing interior angles. o Promotes algebraic setup to find unknown variables. **2. Exterior Angle Theorem Worksheet** o 6 scaffolded questions applying the exterior angle rule. o Includes challenging application problems involving isosceles and equilateral triangles. **3. Interior and Exterior Angles in Regular Polygons Worksheet** o 13 advanced questions focusing on regular polygon properties. o Covers finding interior angle sums, individual interior/exterior angles, and determining the number of sides of polygons (ranging from pentagons to 36-gons). **Core Skills Covered:** • Applying the triangle angle sum rule (interior angles add up to 180 degrees). • Utilizing the exterior angle theorem to solve geometric diagrams. • Working with angles on a straight line and supplementary linear pairs. • Calculating interior and exterior angle measures for various regular polygons using standard geometric formulas. • Formulating and solving multi-step algebraic equations based on visual geometric properties. **Perfect For:** • Key Stage 3 (KS3) Math Classes (Years 7–9) • Key Stage 4 (KS4) & GCSE Foundation and Higher Tiers • IGCSE & International Baccalaureate (IB) Maths Prep • Homework, Classwork, Cover Work, or Exam Revision **Exam Board Alignment:** • Excellent preparation for Edexcel, AQA, OCR, and Cambridge International (CIE) specifications covering properties of polygons, angles, and geometric reasoning. ________________________________________

£2.90
Bundle

Angles Bundle: Parallel Lines, Transversals, Triangle Sum & Exterior Angles

Three worksheets on the following topics: * Triangle Angle Sum Theorem * Exterior Angles of a Triangle * Parallel Lines and Transversals The first worksheet has exercises that aim to to strengthen your students’ skill at finding an unknown angle measure in a triangle, using the triangle angle sum theorem. Using the fact that the sum of the three interior angles of any triangle is 180 degrees, students set up equations and solve for the missing angles. There are 16 problems that vary in level of difficulty. In the first questions students are given a triangle and two of the angle measures, and have to find the missing third angle measure. In the next problems students are given some special types of triangles (right-angled, equilateral and isosceles) and all the required information to set up an equation and solve to find a missing angle. In the last problems, they are given composite shapes consisting of two or more triangles and in order to find the required missing angle they first have to find some other angles. The second worksheet is on the exterior angles of a triangle. The exercises require to use the fact that an exterior angle of a triangle is equal to the sum of the two interior opposite angles. The third worksheet is on angle relationships of angles formed when two lines are cut by a transversal. The following relationships are included: corresponding angles, alternate interior angles, consecutive interior angles, vertical angles and supplementary angles. Introductory and more advanced problems are included. Students practice finding the value of missing angle measures using the angle relationships seen in parallel lines cut by a transversal to form equations and then solve. Detailed solutions are provided. Master geometry angle properties with this complete three-pack worksheet bundle. Designed for Key Stage 3 (KS3) and Key Stage 4 (KS4) GCSE Maths, these practice packs build confidence in parallel lines, transversals, triangle angle sums, and exterior angles. Full step-by-step teacher solutions are included! ________________________________________ **What is Included in this 3-Worksheet Bundle?** 1. Parallel Lines & Transversals Pack: Scaffolded practice moving from basic angle rules to setting up and solving linear algebraic equations using geometric relationships. 2. Triangle Angle Sum Theorem Pack: Features clear layouts testing interior angles across scalene, isosceles, and equilateral triangles. 3. Exterior Angles of a Triangle Pack: Focused worksheets applying the remote interior angle rule to evaluate unknown variables. **Key Topics & Angle Rules Covered** • **Parallel Line Properties:** Corresponding, vertically opposite, alternate, and co-interior (consecutive interior) angles. • **Triangle Properties:** Straight-line rules, angles around a point, base angles of isosceles triangles, and properties of equilateral triangles. • **Algebraic Integration:** Multi-step problems requiring students to form and solve linear equations using geometric relationships. • **Detailed Step-by-Step Worked Solutions:** Comprehensive answer sheets showing every single stage of the calculation—perfect for cover work, busy teachers, or student self-assessment. **Ideal For:** • Independent classroom practice worksheets or homework booklets. • Targeted GCSE Maths exam revision and diagnostic intervention. • Ready-made, no-prep cover lessons or math revision stations.

£3.35

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