Consider a circle divided up into 11 equal sections. How many lines of symmetry will this circle have?
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Solution 1 Imagine 1 1 lines emerging from one point. If n lines emerge from one point, where n is odd, we shall have n lines of symmetry, each one beginning at one line and passing in the middle of two more lines. That makes 1 1 lines of symmetry.
Solution 2 Consider an 1 1 -sided polygon. As discussed in the "Recognizing Symmetry" section of Symmetry , an n -sided polygon has n lines of symmetry.