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Polygon Exterior Angles

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Polygon Exterior Angles worksheet preview

Polygon Exterior Angles

Polygon with exterior angles marked

🎯 WALT: Understand exterior angles of polygons and apply the 360° rule

Success Criteria: I can identify exterior angles, calculate missing angles, and explain why the sum is always 360°

1. What is the sum of exterior angles for ANY polygon?

180°

360°

540°

It depends on the number of sides

2. In a regular pentagon, each exterior angle measures:

36°

72°

108°

144°

3. Which statements about exterior angles are correct? (Tick all that apply)

An exterior angle and its adjacent interior angle sum to 180°

Regular polygons have equal exterior angles

The sum changes based on polygon size

Walking around a polygon, you turn through 360° total

✏️ Calculating Missing Exterior Angles

4. A quadrilateral has exterior angles of 85°, 110°, and 95°. Find the fourth exterior angle.

Answer: __________°

5. In a regular octagon, calculate one exterior angle.

Answer: __________°

6. An irregular hexagon has five exterior angles measuring 45°, 70°, 55°, 80°, and 65°. What is the sixth exterior angle?

Answer: __________°

7. Differentiation Support: Complete this sentence using the word bank:

Word bank: 360°, exterior, vertex, sum, polygon

The ________ of all ________ angles of any ________ is always ________ because walking around the shape involves one complete turn at each ________.

🚀 Extension & Reasoning

8. Explain why the sum of exterior angles is always 360° for any polygon, using the concept of "turning around" the shape.
9. Extension Challenge: If a regular polygon has an exterior angle of 24°, how many sides does it have? Show your working.

Number of sides: __________

10. Advanced Problem: In a regular n-sided polygon, each exterior angle is 40°. Write an equation and solve for n.

Equation: ________________

Solution: n = __________

11. Create your own problem involving exterior angles and solve it:

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