Match the number of triangles formed or the interior angle sum to each regular polygon.
– number of triangles formed is 4
– Interior angle sum is 1,440°
– Interior angle sum is 1,800°
– number of triangles formed is 6
Match the number of triangles formed or the interior angle sum to each regular polygon
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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