Interior angles of polygons

key notes :

🔷 What is an Interior Angle?

• An interior angle is the angle formed inside a polygon at each vertex ✨.

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✅ Sum of Interior Angles Formula

For any polygon with n sides:

Sum of Interior Angles = (n−2) × 180°

📍 Example: For a pentagon (5 sides)
Sum = (5 − 2) × 180° = 540° 🔥

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📐 Interior Angle of a Regular Polygon

A regular polygon has all sides and angles equal 💠.

Each Interior Angle = (n−2)×180° / n

📍 Example: Regular hexagon (6 sides)
Each angle = (6−2)×180° / 6 = 120° 🌟

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🧮 Quick Reference Table

Polygon	Sides (n)	Sum of Interior Angles	Each Angle (Regular)
Triangle 🔺	3	180°	60°
Quadrilateral ⬜	4	360°	90°
Pentagon ⭐	5	540°	108°
Hexagon 🔷	6	720°	120°
Heptagon 🌈	7	900°	~128.57°
Octagon 🛑	8	1080°	135°

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🧠 Why (n − 2)?

• Any polygon can be divided into (n − 2) triangles 🔺🔺🔺
• Each triangle = 180°
• So multiply triangles × 180° ✅

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🚦 Important Tips to Remember

💡 Interior angles increase as the number of sides increases.
💡 Regular polygons have equal interior and exterior angles.
💡 Exterior angle of a regular polygon = 360° ÷ n 🔁
💡 Interior + Exterior angle at a vertex = 180° (Linear pair) 📏

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🏁 Summary

• Interior angle → inside the polygon 🏠
• Sum of interior angles → (n−2) × 180°
• Each angle (regular polygon) → (n−2) × 180°/n

Learn with an example

let’s practice! 🖊️