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AssignmentMultiple Select

Properties of Transformations

Question 6 • TX-Mathematical Models with Applications A

Which of the statements are true regarding the two regular polygons? Check all that apply.

Answer
A
The order of rotational symmetry for the octagon is 8.
B
The dodecagon has a rotational symmetry of 180º.
C
The order of rotational symmetry for the dodecagon is 10.
D
The smallest angle of rotational symmetry for the octagon is 36º.
E
The smallest angle of rotational symmetry for the dodecagon is smaller than the one for the octagon.

Explanation

A regular polygon with n sides has rotational symmetry of order n, and its smallest angle of rotational symmetry is 360° ÷ n. The octagon has order 8 and a smallest angle of 45°, so A is true and D is false. The dodecagon has order 12, not 10, and its smallest angle is 30°; a 180° rotation is also a multiple of 30°, so B and E are true while C is false.

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