4.2 Compare Your Answers 2

Compare your answers.

1. Use the triangle interior angles sum to complete the following table.
   
   

   Polygon	Number of Sides	Number of Triangles	Sketch	Interior Angles Sum
   triangle	3	1		180°
   quadrilateral	4	2		2 × 180° = 360°
   pentagon	5	3
   hexagon	6	4
   heptagon	7	5
   decagon	10	8

2. Look for a pattern in your table. Use this pattern to determine the interior angles sum for
   
   
   1. a hectagon (a 100-sided polygon)
      
      
      If you draw all the possible diagonals from one vertex of a convex polygon, you will get two less triangles than the number of sides.
      
      According to the pattern, a 100-sided polygon could be split into 98 triangles. This means the angle sum will be 98 × 180° = 17 640°.
      
      
      
   2. a myriagon (a 10 000-sided polygon)
      
      According to the pattern, a 10 000-sided polygon could be split into 9998 triangles. This means the angle sum will be 9998 × 180° = 1 799 640°.
      
      
3. Determine an expression that will allow you to find the interior angles sum of
   an n-sided polygon.
   
   
   If you draw all the possible diagonals from one vertex of an n-sided convex polygon, you will have n − 2 triangles. Each triangle has a sum of 180°, so the sum of the interior angles of an n-sided polygon is (n − 2)180°.