Complete the table to show the number of triangles that each polygon can be decomposed into and the interior angle sum for each polygon.
Number of Sides of the Polygon
14
15
16
17
18
Number of Triangles Formed
12
14
Interior Angle Sum
°
2,340°
°
°
°
(Simplify your answers. Do not include the degree symbol in your answers.)
To complete the table, we can use two formulas:
1. Number of triangles formed in a polygon: This is given by the formula ( n – 2 ), where ( n ) is the number of sides.
2. Interior angle sum of a polygon: This is calculated using the formula ( (n – 2) times 180 ).
Now let’s fill in the table step-by-step.
1. Number of Triangles Formed:
– For a polygon with 14 sides: ( 14 – 2 = 12 ) triangles
– For a polygon with 15 sides: ( 15 – 2 = 13 ) triangles
– For a polygon with 16 sides: ( 16 – 2 = 14 ) triangles
– For a polygon with 17 sides: ( 17 – 2 = 15 ) triangles
– For a polygon with 18 sides: ( 18 – 2 = 16 ) triangles
2. Interior Angle Sum:
– For a polygon with 14 sides: ( (14 – 2) times 180 = 12 times 180 = 2160 )
– For a polygon with 15 sides: ( (15 – 2) times 180 = 13 times 180 = 2340 ) (already provided)
– For a polygon with 16 sides: ( (16 –