Answer:
1.260
Step-by-step explanation:
Each time we add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), we add another 180° to the total:
If it is a Regular Polygon (all sides are equal, all angles are equal)
Shape Sides Sum of
Interior Angles Shape Each Angle
Triangle 3 180° regular triangle 60°
Quadrilateral 4 360° regular quadrilateral 90°
Pentagon 5 540° pentagon regular 108°
Hexagon 6 720° hexagon regular 120°
Heptagon (or Septagon) 7 900° heptagon refular 128.57...°
Octagon 8 1080° octagon regular 135°
Nonagon 9 1260° nonagon regular 140°
Any Polygon n (n−2) × 180° regular n gon (n−2) × 180° / n
So the general rule is:
Sum of Interior Angles = (n−2) × 180°
Each Angle (of a Regular Polygon) = (n−2) × 180° / n
Perhaps an example will help:
Example: What about a Regular Decagon (10 sides) ?
regular decagon
Sum of Interior Angles = (n−2) × 180°
= (10−2) × 180°
= 8 × 180°
= 1440°
And for a Regular Decagon:
Each interior angle = 1440°/10 = 144°
Note: Interior Angles are sometimes called "Internal Angles"
