Exterior Angles Exploration

Year 8 Maths — Lesson 1: Exterior Angles and Their Sum

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📐 Part 1: Key Ideas

Remember: An exterior angle is formed by extending one side of a polygon at a vertex. The exterior angle and interior angle at the same vertex add up to 180° (they form a straight line).

1. Circle the correct definition of an exterior angle:

The angle inside a polygon at a vertex

The angle formed outside a polygon when one side is extended

The angle at the centre of a polygon

Half the interior angle

2. An interior angle of a polygon measures 110°. What is the exterior angle at the same vertex?

3. Select ALL statements that are true about exterior angles:

The exterior angle and interior angle at the same vertex add up to 180°

The sum of exterior angles of any polygon is always 360°

Exterior angles are always larger than interior angles

In a regular polygon, all exterior angles are equal

📏 Part 2: Measuring and Calculating Exterior Angles

Use your protractor to measure the exterior angles of the polygons your teacher has given you, then complete the table below.

4. Record your measurements and calculate the sum of exterior angles for each polygon:

Triangle — Exterior angles measured: ______°, ______°, ______°
Sum = ______°

Quadrilateral — Exterior angles measured: ______°, ______°, ______°, ______°
Sum = ______°

Pentagon — Exterior angles measured: ______°, ______°, ______°, ______°, ______°
Sum = ______°

5. What do you notice about the sum of exterior angles for each polygon?

6. A regular hexagon has 6 equal exterior angles and the sum of its exterior angles is 360°. Calculate the size of each exterior angle. Show your working.

7. A regular polygon has exterior angles of 45° each. How many sides does the polygon have? Show your working.

8. One exterior angle of a polygon is missing. The other exterior angles are: 72°, 68°, 95°, 55°, and 40°. Find the missing exterior angle.

💭 Part 3: Reflect and Explain

9. In your own words, explain why the sum of exterior angles of any polygon is always 360°. Think about what happens when you walk all the way around a shape and end up facing the same direction you started. (Hint: think about angles around a full turn.)

10. Challenge: A student says, "A polygon with more sides will have a bigger sum of exterior angles." Do you agree or disagree? Explain your reasoning using evidence from your measurements above.