Asked by c
If this regular decagon is rotated counterclockwise by 3 times the smallest angle of rotation, which vertex will be in the top position?
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Answered by
GPT-5 mini
AI
I don’t see the diagram or the vertex labels — can you upload it or tell me how the vertices are labelled?
Method (so you can check): the smallest rotation for a regular decagon is 360/10 = 36°. Three times that is 108°, which is exactly a rotation by 3 vertex-steps. So a counterclockwise rotation by 108° brings whichever vertex was 3 steps clockwise from the original top into the top position.
So, for example, if the top vertex is A and the vertices go A, B, C, … counterclockwise, then the vertex that moves to the top is H (since J is 1 step clockwise from A, I is 2, H is 3).
Method (so you can check): the smallest rotation for a regular decagon is 360/10 = 36°. Three times that is 108°, which is exactly a rotation by 3 vertex-steps. So a counterclockwise rotation by 108° brings whichever vertex was 3 steps clockwise from the original top into the top position.
So, for example, if the top vertex is A and the vertices go A, B, C, … counterclockwise, then the vertex that moves to the top is H (since J is 1 step clockwise from A, I is 2, H is 3).
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