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Class 7 Rotational Symmetry — practice questions with answers

Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The fixed point about which a figure rotates is called its ____.
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Answer: A) centre of rotation
A figure turns about a fixed point known as the centre of rotation.
2. The angle of rotation of an equilateral triangle is ____.
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Answer: A) 120°
Order = 3, so angle = 360°/3 = 120°.
3. A figure has rotational symmetry of order 8. After turning it by how many degrees does it FIRST look the same?
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Answer: C) 45
Smallest angle = 360°/8 = 45°.
4. A regular star is made by joining points of a regular 5-pointed figure. It looks the same after every 72° turn.
How many distinct positions (including the start) does it show in one full 360° turn?
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Answer: B) 5
360°/72° = 5, so over a full turn it occupies 5 identical positions, i.e. order 5.
5. A symmetric design is formed by placing identical motifs at equal angles around a centre. The angle of rotation is known to be a divisor of 360° that is greater than 24° and less than 40°.
How many possible whole-number angles of rotation are there?
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Answer: A) 2
Divisors of 360 strictly between 24 and 40 are 30 and 36 only, so there are 2 possible whole-number angles.
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