Internal and External Angles of Different Polygons

A polygon is a closed shape made up of straight lines. Examples include triangle, square, pentagon, hexagon, etc. Every polygon has internal angles (inside angles) and external angles (outside angles).

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1. Triangle (3 sides)

Internal Angles:

• Sum of internal angles = 180°
• Example: 60° + 60° + 60° = 180°

External Angles:

• Sum of external angles = 360°
• Each external angle depends on internal angles:
  External angle = 180° − internal angle

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2. Quadrilateral (4 sides)

Internal Angles:

• Sum of internal angles = 360°
• Example: Rectangle = 90° + 90° + 90° + 90° = 360°

External Angles:

• Sum of external angles = 360°

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3. Pentagon (5 sides)

Internal Angles:

• Sum = 540°
• Regular pentagon: each angle = 540° ÷ 5 = 108°

External Angles:

• Sum = 360°
• Each external angle (regular pentagon) = 360° ÷ 5 = 72°

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4. Hexagon (6 sides)

Internal Angles:

• Sum = 720°
• Regular hexagon: each angle = 720° ÷ 6 = 120°

External Angles:

• Sum = 360°
• Each external angle = 360° ÷ 6 = 60°

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5. Heptagon (7 sides)

Internal Angles:

• Sum = 900°
• Regular heptagon: each angle = 900° ÷ 7 ≈ 128.57°

External Angles:

• Sum = 360°
• Each external angle ≈ 360° ÷ 7 ≈ 51.43°

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6. Octagon (8 sides)

Internal Angles:

• Sum = 1080°
• Regular octagon: each angle = 1080° ÷ 8 = 135°

External Angles:

• Sum = 360°
• Each external angle = 360° ÷ 8 = 45°

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Important Rules

✔ Internal Angle Sum Formula:

$$(n – 2) \times 180^\circ$$(n−2)×180∘

✔ External Angle Sum (Any Polygon):

$$360^\circ$$360∘

✔ Each External Angle (Regular Polygon):

$$\frac{360^\circ}{n}$$n360∘​

Internal and External Angles of Different Polygons

Polygon	Number of Sides (n)	Sum of Internal Angles	Each Internal Angle (Regular)	Sum of External Angles	Each External Angle (Regular)
Triangle	3	180°	60°	360°	120°
Quadrilateral	4	360°	90°	360°	90°
Pentagon	5	540°	108°	360°	72°
Hexagon	6	720°	120°	360°	60°
Heptagon	7	900°	≈128.57°	360°	≈51.43°
Octagon	8	1080°	135°	360°	45°

Important Formulas

Type	Formula
Sum of internal angles	(n − 2) × 180°
Sum of external angles	360°
Each external angle (regular polygon)	360° ÷ n