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Polygon Exterior Angles
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Polygon Exterior Angles
📚 Part 1: Understanding Exterior Angles
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, what is the measure of each exterior angle?
60°
72°
108°
120°
3. A regular polygon has exterior angles of 40°. How many sides does it have?
8 sides
9 sides
10 sides
12 sides
4. Which statements about exterior angles are true? (Select all that apply)
An exterior angle and its adjacent interior angle are supplementary
The sum of exterior angles changes as the polygon gets larger
Walking around a polygon, you turn through 360° total
Exterior angles are always acute
✏️ Part 2: Problem Solving
5. An irregular quadrilateral has exterior angles of 85°, 95°, and 110°. Find the fourth exterior angle.
Answer: _________°
6. Explain why the sum of exterior angles is always 360° for any polygon. Use the idea of "turning around" in your explanation.
7. A regular octagon has each exterior angle measuring _____°. Show your working:
8. Extension: If a regular polygon has an exterior angle of 24°, what is the measure of each interior angle?
Answer: _________°
🎯 Part 3: Application Challenge
9. Draw and label the exterior angles of a triangle. Verify that they sum to 360°.
10. Advanced Challenge: A polygon has exterior angles in the ratio 2:3:4:3. If this is a quadrilateral, find each exterior angle.
The four exterior angles are: _____°, _____°, _____°, and _____°
11. Real-world connection: A robot walks around a hexagonal garden bed, turning at each corner. What is the total amount it turns through? Explain your reasoning.
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