# Polygon

See how to find the angles of a polygon.

5 examples and their solutions.

## Polygon Names

Name | Number of Angles/Sides |
---|---|

Triangle | 3 |

Quadrilateral | 4 |

Pentagon | 5 |

Hexagon | 6 |

Heptagon | 7 |

Octagon | 8 |

Nonagon | 9 |

Decagon | 10 |

n-gon | n |

## Interior Angles of a Polygon

### Formula

n-gon

(sum) = 180⋅(n - 2)°

(sum) = 180⋅(n - 2)°

### Example

Heptagon

Sum of the measures of the interior angles?

Solution Sum of the measures of the interior angles?

n = 7 - [1]

(sum) = 180⋅5

= 900

(sum) = 180⋅5

= 900

[1]

Heptagon → 7 angles

Close

### Example

Regular octagon

Measure of an interior angle?

Solution Measure of an interior angle?

n = 8 - [1]

(sum) = 180⋅6

= 1080

(angle) = 10808 - [2] [3]

= 135°

(sum) = 180⋅6

= 1080

(angle) = 10808 - [2] [3]

= 135°

[1]

Octagon → 8 interior angles

[2]

Regular octagon

→ 8 congruent sides/angles

→ 8 congruent sides/angles

[3]

Sum of the interior angles: 1080°

8 congruent interior angles

So the measure of an interior angle is

1080/8.

8 congruent interior angles

So the measure of an interior angle is

1080/8.

Close

## Exterior Angles of a Polygon

### Formula

(sum) = 360°

### Example

3x + 40 + 2x + 10 + 120 + 90 = 360

5x + 260 = 360

5x = 100

x = 20

Close

### Example

Regular pentagon

Measure of an exterior angle?

Solution Measure of an exterior angle?

n = 5 - [1]

(sum) = 360

(angle) = 3605 - [2]

= 72°

(sum) = 360

(angle) = 3605 - [2]

= 72°

[1]

Pentagon → 5 angles

[2]

The sum of the exterior angles is 360°.

A regular pentagon

→ 5 congruent interior angles

→ 5 congruent exterior angles

So the measure of an exterior angle is

360/5.

A regular pentagon

→ 5 congruent interior angles

→ 5 congruent exterior angles

So the measure of an exterior angle is

360/5.

Close

### Example

Regular polygon

Measure of an exterior angle: 60°

Name of the polygon?

Solution Measure of an exterior angle: 60°

Name of the polygon?

(sum) = 360

(angle) = 60

n = 36060 - [1]

= 6

→ Hexagon

(angle) = 60

n = 36060 - [1]

= 6

→ Hexagon

[1]

n = (number of sides)

= (number of interior angles)

= (number of exterior angles)

= (number of interior angles)

= (number of exterior angles)

Close