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Polygon Interior Angles
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Polygon Interior Angles
📐 Part 1: Understanding the Formula
1. The formula for the sum of interior angles of a polygon is (n - 2) × 180°, where n is the number of sides. What is the sum of interior angles for each polygon?
a) Triangle (3 sides): ___________
b) Quadrilateral (4 sides): ___________
c) Pentagon (5 sides): ___________
d) Hexagon (6 sides): ___________
2. Which polygon has an interior angle sum of 1080°?
Heptagon (7 sides)
Octagon (8 sides)
Nonagon (9 sides)
Decagon (10 sides)
3. Show your working to find the sum of interior angles of a 12-sided polygon:
🔍 Part 2: Finding Missing Angles
4. A quadrilateral has interior angles of 85°, 110°, and 95°. What is the fourth angle?
5. In a pentagon, four of the interior angles are 108°, 112°, 95°, and 118°. Calculate the fifth angle.
6. A hexagon has five equal interior angles of 120° each. What is the sixth angle?
120°
100°
140°
130°
💭 Part 3: Reasoning and Problem Solving
7. Explain in your own words why the formula for interior angles is (n - 2) × 180°. Think about how polygons can be divided into triangles.
8. A regular polygon has interior angles of 140° each. How many sides does it have?
9. True or False: The sum of interior angles increases by 180° for each additional side added to a polygon.
True
False
Explain your answer: ________________________________
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