polygons

• Polygon

  2D shape with straight sides
• Regular polygon

  Every side is equal, every angle is equal
• Regular polygons

  • Equilateral triangle
  • Square
  • Regular pentagon
• Irregular polygon

  Sides and angles are not equal
• Angle sum of a triangle is 180 degrees
• Angle sum of a quadrilateral is 360 degrees
• Angle sum of a pentagon is 540 degrees
• Angle sum of a hexagon is 720 degrees
• Angle sum formula for a polygon

  n - 2 x 180 degrees, where n is the number of sides
• Interior angle of a regular polygon

  (n - 2) x 180 / n, where n is the number of sides
• Exterior angle of a polygon

  180 degrees - Interior angle
• Sum of all exterior angles of any polygon is 360 degrees
• Exterior angle of a regular polygon

  360 / n degrees, where n is the number of sides
• Finding missing angle in an irregular pentagon

  1. Angle sum of pentagon is 540 degrees

  2. Add up known angles

  3. Subtract known angles from 540 to get missing angle
• Finding missing angle in an irregular hexagon

  1. Angle sum of hexagon is 720 degrees

  2. Add up known angles

  3. Subtract known angles from 720 to get missing angle
• Regular octagon and regular hexagon

  • Exterior angle of octagon is 45 degrees
  • Exterior angle of hexagon is 60 degrees
  • Missing angle x = 45 + 60 = 105 degrees
• Two regular pentagons and another regular polygon P

  • Interior angle of pentagon is 108 degrees
  • Sum of known angles is 216 degrees
  • Interior angle of polygon P is 360 - 216 = 144 degrees
  • Exterior angle of polygon P is 180 - 144 = 36 degrees
  • Number of sides of polygon P is 360 / 36 = 10