Through what angle must it turn to match itself again?
A normal-level "Angle" problem.The turn that brings a shape back onto itself is "a full turn ÷ the number of corners". It is a different measure from the fold-lines of reflection, and both gauge the symmetry of a regular polygon.
GivenA regular 5-sided polygon is turned about its centre.
Hints
- First, be clear about what "matching" means. The blue outline is the shape turned a little — its corners land nowhere near the original ones, so it does not match.
- To match, every corner must land exactly on a corner. The smallest such turn moves corner A onto its neighbour B.
- That angle is easy to see from the centre: the 5 corners are evenly spaced, so it is 360° shared out 5 ways: 360 ÷ 5 = 72°.
- Check it. Turned by 72°, A goes to B, B goes to C, and so on — every corner shifts along by one, and the red shape lands exactly on the original.
- The smallest is 72°, and it matches again at 72°, 144°, 216°, 288°, 360°. For any regular n-gon it is 360 ÷ n: 120° for a triangle, 90° for a square. More corners means a smaller angle — and a circle matches at every angle.
Answer 72度
More "Angle" problems
- How big is angle x?
- How many degrees is angle x?
- What is A＋B＋C＋D＋E?
- How big is angle BIC?
- How many degrees is angle x?
- How many degrees is angle x?
Browse by idea
- Chasing angles — there are only four tools
- Decide how to count, then count
- Fold it, turn it, copy it across