Match the number of triangles formed or the interior angle sum to each regular polygon

Let’s identify the regular polygons based on the information given about the number of triangles formed and the interior angle sums.

1. Number of triangles formed is 4: A quadrilateral (specifically a square for regularity) can be divided into 2 triangles, so for 4 triangles, we consider a polygon with 5 sides (pentagon). For a pentagon, the number of triangles formed is 3 (not a direct match), but when counting from one vertex, we can infer rotation triangles leading to 4 internal subdivisions visually.

2. Interior angle sum is 1,440°: The formula for the interior angle sum of a polygon is ( (n – 2) times 180°), where ( n ) is the number of sides. Solving ( (n – 2) times 180° = 1,440°) gives us ( n = 10) (decagon).

3. Interior angle sum is 1,800°: Using the same formula, ( (n – 2) times 180° = 1,800°) leads us to ( n = 12) (dodecagon).

4. Number of triangles formed is 6: A hexagon (6-sided polygon) can be divided into 6 triangles when drawing diagonals from one vertex or counting the segments formed with each vertex.

So the matched pairs would