Definitions [3]
Definition: Polygon
A polygon is any closed, flat shape that is formed by straight line segments (sides).
Example:
- Dimension: Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
- Zero-dimensional: A point is a zero-dimensional object as it has no length, width, or height. It has no size. It tells about the location only. A point is dimensionless.
- One Dimensional: A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
- The 2-dimensional shapes or Plane Figures: The 2-dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width.
- The 3-dimensional shapes or solid object: A solid object has three measurements like length, breadth, height, or depth. Hence, they are called three-dimensional shapes. Also, a solid object occupies some space
Right Angle: The right angle is exactly equal to 90°.
Straight Angle: A straight angle is equal to 180°.
Revolution: Turning by two straight angles (or four right angles) in the same direction makes a full turn. This one complete turn is called one revolution.
Complete Angle: The angle for one revolution is a complete angle. A complete angle is one complete revolution or equal to 360°.
Formulae [1]
Formula: Sum of Interior Angles
Sum of interior angles of a polygon = (n – 2) × 180°
Explanation:
- A polygon with n sides can be divided into smaller triangles by drawing diagonals from one vertex.
- Each triangle has a total angle sum of 180°.
- Since the number of triangles formed inside the polygon is (n – 2).
- The total sum of all interior angles is therefore (n – 2) × 180°.
