Study guides › Level 7 · Geometry

Angles inside a polygon

Level 7 · Geometry · for questions like “What do the inside angles of a hexagon add up to?”

💡 The idea

From one corner, a shape with n sides splits into n − 2 triangles. Each triangle holds 180°.

angle sum = (n − 2) × 180°

🪜 The steps

1. Count the sides (n).
2. Take away 2, then multiply by 180.

✏️ Worked examples

1. Hexagon (6 sides): 4 × 180 = 720°.

2. Decagon (10 sides): 8 × 180 = 1,440°.

⚠️ Watch out

• It's n − 2, not n. A square is 2 triangles (360°), not 4.

🎯 Try these

1. Pentagon (5 sides)
2. Octagon (8 sides)
3. 12 sides

Answers: 1) 540° 2) 1,080° 3) 1,800°

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.