Year 8 - Maths
Exterior angles of polygons
Geometrical properties: polygons
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will investigate internal and external angles of polygons and angles made with a transveral and parallel lines. Pupils will develop their ability to formally prove properties of polygons to generalise.
Lesson Summary
You will learn to find the sum of the exterior angles of a polygon.
Key Notes
- The sum of the exterior angles of a polygon can be demonstrated using a point.
- The sum of the exterior angles of a polygon can be proven using interior angles and the angles on a straight line.
- The angle sum of a triangle can also be proven using exterior angles .
- The size of the exterior angle of any polygon can be found using the sum of angles.
Vocabulary To Learn
- Interior angle: an angle formed inside a polygon by two of its edges.
- Exterior angle: an angle on the outside of a polygon between an extension of an edge and its adjacent edge.
- Supplementary angle: a pair of angles that sum to 180°.
Common Mistakes To Avoid
- The exterior angle is the entire reflex angle that is on the outside of each vertex of a shape.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The sum of the exterior angles of a polygon can be demonstrated using a point. The sum of the exterior angles of a polygon can be proven using interior angles and the angles on a straight line.
2. Use this key word in a maths sentence and explain it clearly. 'Interior angle'
an angle formed inside a polygon by two of its edges. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The exterior angle is the entire reflex angle that is on the outside of each vertex of a shape. Correction: Ask a pupil to stand and walk around the room to trace a shape. The angle that the pupil turns at each vertex is an exterior angle.
More Lessons In This Unit
- Alternate angles Study Guide
- Angles on parallel lines traversed by a straight line Study Guide
- Checking understanding of angles from KS2 Study Guide
- Co-interior angles Study Guide
- Corresponding angles Study Guide
- Deriving the sum of interior angles in multiple ways Study Guide
- Formal angle notation Study Guide
- Formalising understanding of triangles from KS2 Study Guide
- Interior and exterior angles of regular polygons Study Guide
- Interior angles of a polygon Study Guide
- Missing angles Study Guide
- Problem solving with polygons Study Guide
- Securing understanding of angles from KS2 Study Guide
- The sum of the interior angles of any triangle Study Guide
- Using the sum of the interior angles of a triangle Study Guide
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