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Auralith Learning

Year 8 · Maths · Angles in polygons · Lesson 3

Exterior angles of polygons

Use the fact that exterior angles add up to 360° to find exterior and interior angles of regular polygons and the number of sides.

Whiteboard video lesson: Exterior angles of polygons

26-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand exterior angles
  • Know exterior angles add up to 360°
  • Find exterior angles of regular polygons
  • Use exterior angles to find interior angles
  • Find the number of sides of a regular polygon

The method

  1. Exterior angles of any polygon add up to 360°.
  2. Regular polygon: exterior angle = 360° ÷ number of sides.
  3. Interior angle = 180° − exterior angle.
  4. Number of sides = 360° ÷ exterior angle.

Key words: exterior angle, interior angle, regular polygon, 360°, sides.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Find the size of each exterior angle of a regular quadrilateral.

  1. Step 1: Exterior angles add up to 360°.
  2. Step 2: 4 equal exterior angles
  3. Step 3: 360° ÷ 4 = 90°

Answer: 90°

Question 2

Find the size of each exterior angle of a regular hexagon.

  1. Step 1: Exterior angles add up to 360°.
  2. Step 2: 6 equal exterior angles
  3. Step 3: 360° ÷ 6 = 60°

Answer: 60°

Question 3

Find the size of each exterior angle of a regular decagon.

  1. Step 1: Exterior angles add up to 360°.
  2. Step 2: 10 equal exterior angles
  3. Step 3: 360° ÷ 10 = 36°

Answer: 36°