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
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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.
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Exterior Angles of a Polygon
Formula
(sum) = 360°
Example
3x + 40 + 2x + 10 + 120 + 90 = 360
5x + 260 = 360
5x = 100
x = 20
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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.
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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)
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