A pentagon has actually 5 sides, and also can be made native three triangles, so you understand what ...
You are watching: Find the sum of the angle measures of a nonagon
... Its inner angles add up to 3 × 180° = 540°
And when it is regular (all angle the same), climate each angle is 540° / 5 = 108°
(Exercise: make certain each triangle below adds approximately 180°, and check that the pentagon"s inner angles add up come 540°)
The inner Angles of a Pentagon add up to 540°
The general Rule
Each time we add a side (triangle to quadrilateral, square to pentagon, etc), us add another 180° come the total:
| If it is a Regular Polygon (all sides space equal, all angles room 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: Which Of The Following Compounds Contains An Ionic Bond? ? Chem 5 Flashcards | ... |
| Any Polygon | n | (n−2) × 180° |  | (n−2) × 180° / n |
So the general ascendancy is:
Sum of inner Angles = (n−2) × 180°
Each angle (of a regular Polygon) = (n−2) × 180° / n
Perhaps an instance will help:
Example: What around a continual Decagon (10 sides) ?
Sum of interior Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°
And for a continual Decagon:
Each inner angle = 1440°/10 = 144°
Note: internal Angles are sometimes dubbed "Internal Angles"
interior Angles Exterior Angles degrees (Angle) 2D shapes Triangles quadrilateral Geometry Index