Which regular polygon would carry onto itself after a rotation of 300^(@) about its center? (A) decagon (B) nonagon (C) octagon (D) hexagon

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Which regular polygon would carry onto itself after a rotation of  300^(@) about its center? (A) decagon (B) nonagon (C) octagon (D) hexagon

Bytelearn · Accepted Answer

Calculate Angle of Rotation: To determine which regular polygon would carry onto itself after a rotation of 300 degrees about its center, we need to find a polygon whose angle of rotational symmetry is a factor of 300 degrees. The angle of rotational symmetry for a regular polygon is 360 degrees divided by the number of sides (n).Check Divisibility for Each Polygon: For a regular polygon to carry onto itself after a 300-degree rotation, 360/n should be a divisor of 300. This means that 300 divided by (360/n) should be a whole number.Decagon: Let's check each option: For a decagon (10 sides), the angle of rotational symmetry is 360/10 = 36 degrees. 300 divided by 36 is not a whole number.Nonagon: For a nonagon (9 sides), the angle of rotational symmetry is 360/9 = 40 degrees. 300 divided by 40 is not a whole number.Octagon: For an octagon (8 sides), the angle of rotational symmetry is 360/8 = 45 degrees. 300 divided by 45 is not a whole number.Hexagon: For a hexagon (6 sides), the angle of rotational symmetry is 360/6 = 60 degrees. 300 divided by 60 is exactly 5, which is a whole number.Therefore, a hexagon would carry onto itself after a rotation of 300 degrees about its center because its angle of rotational symmetry is a factor of 300.

Which regular polygon would carry onto itself after a rotation of $300^{\circ}$ about its center? $\newline$ (A) decagon $\newline$ (B) nonagon $\newline$ (C) octagon $\newline$ (D) hexagon

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Which regular polygon would carry onto itself after a rotation of 300∘ 300^{\circ} 300∘ about its center?\newline(A) decagon\newline(B) nonagon\newline(C) octagon\newline(D) hexagon

Which regular polygon would carry onto itself after a rotation of $300^{\circ}$ about its center? $\newline$ (A) decagon $\newline$ (B) nonagon $\newline$ (C) octagon $\newline$ (D) hexagon