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Question
Use the image to answer the question.
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon.
Decompose the decagon into n−2
triangles.
(1 point)
Responses
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and C, A and D, A and E, A and F, A and G, A and H, and A and I.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and C, A and D, A and E, A and F, A and G, A and H, and A and I.
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and E, C and I, D and H, and G and J.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and E, C and I, D and H, and G and J.
An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, C and H, D and I, and E and J. All the lines intersect at a point in the middle of the decagon.
Image with alt text: An illustration shows a decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, C and H, D and I, and E and J. All the lines intersect at a point in the middle of the decagon.
An illustration shows an decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, and D and I. All the lines intersect at a point in the middle of the decagon.
Image with alt text: An illustration shows an decagon. Starting with the top left vertex, the vertices are labeled A, B, C, D, E, F, G, H, I, and J moving clockwise around the polygon. Lines inside the decagon connect the vertices A and F, B and G, and D and I. All the lines intersect at a point in the middle of the decagon.
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To decompose a polygon into triangles, the formula \( n - 2 \) can be used, where \( n \) is the number of sides (or vertices) in the polygon.
For a decagon, which has 10 sides, the calculation would be:
\[
n - 2 = 10 - 2 = 8
\]
This means you can decompose a decagon into 8 triangles.
Looking at the descriptions of the images, the first option where lines connect vertex A to multiple other vertices creates multiple triangles and results in a clear decomposition.
Therefore, the best response from the choices provided would be the first illustration you described, which shows lines connecting vertex A to other vertices, creating the necessary triangles.
Bot GPT 4-o mini 
1 answer