A pentagon has actually 5 sides, and also can be made native three triangles, so you understand what ...
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... Its inner angles add up come 3 × 180° = 540°
And when it is regular (all angles the same), then each angle is 540° / 5 = 108°
(Exercise: make certain each triangle right here adds as much as 180°, and also check the the pentagon"s inner angles add up come 540°)
The inner Angles the a Pentagon include up come 540°
The basic Rule
Each time we add a next (triangle come quadrilateral, quadrilateral to pentagon, etc), we add one more 180° to the total:
| If that is a Regular Polygon (all sides are equal, all angles are equal) | ||||
| Triangle | 3 | 180° |  | 60° |
| Quadrilateral | 4 | 360° |  | 90° |
| Pentagon | 5 | 540° |  | 108° |
| Hexagon | 6 | 720° |  | 120° |
| Heptagon (or Septagon) | 7 | 900° |  | 128.57...° |
| Octagon | 8 | 1080° |  | 135° |
| Nonagon | 9 | 1260° |  | 140° |
| ... | ... | .. | ... See more: Middle School Math With Pizzazz Book A Th With Pizzazz Book A Pdf | ... |
| Any Polygon | n | (n−2) × 180° |  | (n−2) × 180° / n |
So the general rule is:
Sum of internal Angles = (n−2) × 180°
Each edge (of a continuous Polygon) = (n−2) × 180° / n
Perhaps an example will help:
Example: What about a continual Decagon (10 sides) ?
Sum of inner Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°
And for a regular Decagon:
Each inner angle = 1440°/10 = 144°
Note: inner Angles are sometimes called "Internal Angles"
interior Angles Exterior Angles degrees (Angle) 2D forms Triangles quadrilateral Geometry Index