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 match the given numbers to the correct regular polygons:
1. Number of triangles formed is 4: This corresponds to a hexagon. In a hexagon, you can draw 4 triangles by connecting the center to each vertex.
2. Interior angle sum is 1,440°: This corresponds to a dodecagon (12-sided polygon). The formula for the interior angle sum of a polygon is ((n-2) times 180°), where (n) is the number of sides. For a dodecagon, ((12-2) times 180° = 10 times 180° = 1,800°).
3. Interior angle sum is 1,800°: This corresponds to a decagon (10-sided polygon). ((10-2) times 180° = 8 times 180° = 1,440°).
4. Number of triangles formed is 6: This is for a heptagon (7-sided polygon). In a heptagon, you can form 6 triangles by drawing lines from one vertex to each of the non-adjacent vertices.
So the matches are:
– 4 triangles: Hexagon
– 1,440°: Dodecagon
– 1,800°: Decagon
– 6 triangles: