a regular decagon has reflection symmetry and/or rotational symmetry. If it has reflection symmetry, state the number of axes of symmetry. If it has rotation symmetry, state the angle of rotation | Math Questions & Answers

A regular decagon has both rotational and reflection symmetry. To begin with let's look at rotational symmetry. Rotational symmetry means how many degrees can you rotate the decagon until it matches up and looks exactly the same. Since this is a decagon there are ten different positions in which this would work. Remember that there are 360 degrees in one full rotation? Therefore if you take 360 and divide by ten you will get 36. So a regular decagon has rotational symmetry with a 36 degree angle of rotation. Keep in mind the decagon must be regular which mean the sides are all congruent and the angles are all equals. Reflection symmetry means that you can fold the shape in half and it will match up perfectly. For a regular decagon you could draw a line from a vertex across the shape to another vertex and fold along this line. You will end up with 5 axes of symmetry.

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