New
New
Year 10
Higher

Checking and securing understanding of exterior angles

I can find the exterior angle of any regular polygon or deduce the exterior angle of an irregular polygon.

New
New
Year 10
Higher

Checking and securing understanding of exterior angles

I can find the exterior angle of any regular polygon or deduce the exterior angle of an irregular polygon.

Lesson details

Key learning points

  1. The sum of the exterior angles of a polygon can be demonstrated using a point.
  2. The sum of the exterior angles of a polygon can be proven using interior angles and the angles on a straight line.
  3. An exterior and interior angles pair are supplementary.

Common misconception

An exterior angle is equal to 360° - the size of the interior angle because angles around a point sum to 360°.

An exterior angle is an angle on the outside of a polygon between an extension of an edge and the adjacent edge.

Keywords

  • Polygon - A polygon is a flat (2D), closed figure made up of straight line segments.

  • Regular - A regular polygon has sides that are all 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 the adjacent edge.

This lesson makes use of a GeoGebra activity involving commanding a turtle. Pupils would benefit from being able to access this activity and use it throughout the lesson. If this is not possible during the lesson, the link can be shared so pupils can investigate after the lesson.
Teacher tip

Licence

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).

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6 Questions

Q1.
An angle is an angle formed inside a polygon by two of its edges.
Correct Answer: interior
Q2.
Three of the interior angles of a quadrilateral are 80°, 90° and 45°. The size of the fourth interior angle is °.
Correct Answer: 145, one hundred and forty five
Q3.
The interior angles of a dodecagon (12 sides) sum to °.
Correct Answer: 1800, one thousand eight hundred
Q4.
Each interior angle of a regular octagon is °.
Correct Answer: 135, one hudred and thirty five
Q5.
A regular polygon has interior angles of size 162°. The polygon has sides.
Correct Answer: 20, twenty
Q6.
Which interior angles are possible in a regular polygon?
154.5
Correct answer: 156
Correct answer: 157.5
Correct answer: 160

6 Questions

Q1.
An angle is an angle on the outside of a polygon between an extension of an edge and the adjacent edge.
Correct Answer: exterior
Q2.
The exterior angles of any polygon sum to °.
Correct Answer: 360, three hundred and sixty
Q3.
An interior angle and its adjacent exterior angle sum to °.
Correct Answer: 180, one hundred and eighty
Q4.
The size of each exterior angle of a regular pentagon is °.
Correct Answer: 72, seventy two
Q5.
A regular polygon has exterior angles of 40°. The polygon has sides.
Correct Answer: 9, nine, nine (nonagon), 9 (nonagon)
Q6.
Which of these exterior angles are possible for a regular polygon?
Correct answer: 30
Correct answer: 45
Correct answer: 60
75
Correct answer: 90