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HOW MANY PAIRS OF PARALLEL SIDES DO THE FOLLOWING SHAPES HAVE? A) REGULAR
HEPTAGON B) REGULAR OCTAGON C) REGULAR HEXAGON

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Asked in United Kingdom



EXPERT VERIFIED SOLUTION

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ANSWER

The number of pairs of parallel sides are as follows:

 * Regular heptagon: 0
 * Regular octagon: 4
 * Regular hexagon: 3.


EXPLANATION

 1. Analyze the definition of parallel sides within polygons.
    
    * A regular heptagon has 7 sides of equal length, but no sides are parallel
      because each exterior angle is not 180 degrees, meaning the sides will
      never be parallel to each other.
    * A regular octagon has 8 sides of equal length. Considering its geometry,
      there will be pairs of opposite sides that are parallel to each other.
    * A regular hexagon has 6 sides of equal length. Similar to the octagon,
      there will be pairs of opposite sides that are parallel.

 2. Determine the number of pairs of parallel sides for each shape.
    
    * For the regular heptagon, since no sides are parallel, it has 0 pairs of
      parallel sides.
    * For the regular octagon, we need to calculate how many pairs of opposite
      sides are parallel.
    * For the regular hexagon, we also need to calculate how many pairs of
      opposite sides are parallel.

Let's calculate for the octagon and hexagon.
03. Present the final answers for each shape.

- For a regular heptagon, the number of pairs of parallel sides is 0.
- For a regular octagon, the number of pairs of parallel sides is 4.
- For a regular hexagon, the number of pairs of parallel sides is 3\.


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