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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. For a regular pentagon, what is each exterior angle?
60°
72°
108°
120°
3. In a triangle, two exterior angles are 110° and 95°. What is the third exterior angle?
Answer: ___________°
4. A regular polygon has exterior angles of 40° each. How many sides does it have?
Number of sides: ___________
✏️ Part 2: Problem Solving
5. An irregular hexagon has exterior angles of 45°, 80°, 55°, 70°, and 65°. Find the sixth exterior angle.
Sixth exterior angle = ___________°
6. Explain why the sum of exterior angles is always 360° for any polygon. Use the idea of "walking around" the polygon.
7. Complete the table for regular polygons:
| Polygon | Number of Sides | Each Exterior Angle |
|---|---|---|
| Square | 4 | _______° |
| Regular octagon | 8 | _______° |
| Regular decagon | 10 | _______° |
🌟 Part 3: Extension Challenge
8. Advanced: A regular polygon has an exterior angle of 24°. What is the sum of its interior angles?
Sum of interior angles = ___________°
9. Extension: Write a formula to find each exterior angle of a regular n-sided polygon.
10. Reflection: How does understanding exterior angles help you solve problems with interior angles?
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