Polygon Sides Calculation

• What is a side in a polygon?

  A straight line forming the polygon
• What is the sum of the interior angles of a hexagon?

  $720^{\circ}$
• What defines a regular polygon?

  All sides and angles are equal
• What is a vertex in polygon terminology?

  A point where two sides meet
• What are the key concepts related to external angles in polygons?

  • Sum of External Angles: $360^{\circ}$
  • Number of Sides (n): 6
  • One External Angle: $60^{\circ}$
• How do you calculate one external angle in a regular polygon?

  $\text{One External Angle} =$$\frac{360^{\circ}}{n}$
• What is the relationship between an interior angle and its corresponding exterior angle?

  They add up to 180°
• What are external angles in a polygon?

  Angles extending from the outside of a polygon
• How do you calculate the sum of interior angles for a polygon with 6 sides?

  Substitute $n =$$6$ into the formula
• What is the measure of each interior angle in a regular pentagon?

  108°
• What is the external angle formula?

  $\text{Sum of External Angles} =$$360^{\circ}$
• What is the first step to calculate the sum of interior angles of a polygon?

  Identify the number of sides (n)
• What is the relationship between the number of sides and the sum of interior angles?

  More sides result in a larger sum
• What is the measure of one external angle in a regular hexagon?

  $60^{\circ}$
• What are the characteristics of common polygons?

  • Triangle: 3 sides, 3 vertices
  • Square: 4 sides, 4 vertices
  • Pentagon: 5 sides, 5 vertices
  • Hexagon: 6 sides, 6 vertices
• What is an angle in the context of polygons?

  The space between two sides at a vertex
• What is the summary of angle measures for a regular pentagon?

  • Each Interior Angle: 108°
  • Each Exterior Angle: 72°
• What is the sum of all external angles in any polygon?

  $360^{\circ}$
• Why do we subtract 2 from the number of sides in the formula?

  To account for the triangles formed
• If a polygon has 5 sides, what is the sum of its interior angles?

  $540^{\circ}$
• What does the formula $\sum =$$(n - 2) \times 180^{\circ}$ represent?


  The sum of interior angles in a polygon
• How do you identify the number of sides in a polygon?

  Count the edges of the polygon
• What is the result of $(6 - 2) \times 180^{\circ}$?


  $720^{\circ}$
• What is the relationship between the exterior angle and interior angle in this diagram?

  • The exterior angle and interior angle are supplementary, meaning they add up to 180 degrees.
  • The exterior angle is the angle outside the shape, while the interior angle is the angle inside the shape.
• If the exterior angle is $x$ degrees, what is the value of the interior angle?


  $180 - x$ degrees
• What is the measure of each exterior angle in a regular pentagon?

  72°
• How do you calculate the sum of all interior angles in a polygon with n sides?

  $\sum =$$(n - 2) \times 180^{\circ}$
• For a regular hexagon, how is each external angle calculated?

  By dividing $360^{\circ}$ by 6
• If a polygon has 6 sides, what is the value of n?

  $n =$$6$
• How do you find the measure of one external angle in a regular polygon?

  Divide $360^{\circ}$ by the number of sides
• What do interior angles and exterior angles form together?

  A linear pair
• What are the two angles labeled in the image?

  Exterior angle, interior angle
• How does the number of sides in a polygon affect the sum of its interior angles?

  More sides increase the sum of angles
• How can the relationship between the exterior and interior angles be used to solve geometric problems?

  • By knowing that the exterior and interior angles are supplementary, you can use this relationship to:
  • Find the measure of an unknown angle if the other angle is known
  • Determine properties of polygons and other geometric shapes
  • Solve for missing angles in more complex geometric configurations