Year 8 - Maths
Interior and exterior angles of regular 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 interior and exterior angles of regular polygons.
Key Notes
- Exterior angles of a regular polygon are equal.
- The size of the exterior angle of a regular polygon can be determined.
- Interior angles of regular polygons are equal.
- The size of the interior angle of a regular polygon can be determined.
- The number of sides in a regular polygon can be determined from the size of the interior or exterior angle.
Vocabulary To Learn
- Polygon: A polygon is a flat (2D), closed figure made up of straight line segments.
- Regular polygon: A regular polygon has sides that are equal and interior (inside) angles that are all equal.
- Interior angle: An interior angle is an angle formed inside a polygon by two of its edges.
- Exterior angle: An exterior angle is an angle on the outside of a polygon between an extension of an edge and its adjacent edge.
Common Mistakes To Avoid
- Pupils may solve angle problems by using methods which are less efficient than others.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Exterior angles of a regular polygon are equal. The size of the exterior angle of a regular polygon can be determined.
2. Use this key word in a maths sentence and explain it clearly. 'Polygon'
A polygon is a flat (2D), closed figure made up of straight line segments. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may solve angle problems by using methods which are less efficient than others. Correction: While less efficient methods are fine, encourage pupils to review their work each time they solve a problem to consider alternative methods.
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
- Exterior angles of polygons Study Guide
- Formal angle notation Study Guide
- Formalising understanding of triangles from KS2 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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