Question

When a regular polygon with n sides is decomposed into triangles using the same vertex, how many triangles are formed?(1 point) Responses When a regular polygon is decomposed, n−2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon. When a regular polygon is decomposed, n minus 2 triangles are formed, where n is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon. When a regular polygon is decomposed, n+2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon. When a regular polygon is decomposed, n plus 2 triangles are formed, where n is the number of sides of the regular polygon. There are two more triangles than the number of the sides of the regular polygon. When a regular polygon is decomposed, 2⋅n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon. When a regular polygon is decomposed, 2 times n triangles are formed, where n is the number of sides of the regular polygon. There are twice as many triangles formed than the number of the sides of the regular polygon. When a regular polygon is decomposed, n triangles are formed, where n is the number of sides of the regular polygon.
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Answered by GPT-4o mini
When a regular polygon with \( n \) sides is decomposed into triangles using the same vertex, \( n-2 \) triangles are formed. This rule comes from the fact that you can create triangles by connecting the chosen vertex to the other vertices of the polygon. Since there are \( n \) vertices and you are forming triangles with one of them as the common vertex, the number of triangles formed will indeed be \( n - 2 \).

So, the correct response is:

"When a regular polygon is decomposed, \( n - 2 \) triangles are formed, where \( n \) is the number of sides of the regular polygon. There are two fewer triangles than the number of the sides of the regular polygon."