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:

ShapeSidesSum ofInterior AnglesShapeEach Angle
 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