In 1845, pioneers in Utah constructed wagon wheels so that front wheels and rear wheels had a different number of evenly spaced spokes. Spokes are rods that extend from the center of the wheel to the circular traction surface of the wheel.
a. If a rear wheel had exactly seven axes of reflection symmetry, then how many spokes were used and how many rotation symmetries did the wheel have?
b. If the measure of the angle between two adjacent front-wheel spokes was 30°, then how many spokes were used and how many axes of reflection symmetry did the wheel have?
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