Self Check Answers

1. The measure of an exterior angle of a regular decagon is 36°, so each interior angle measures 144°. But 144 does not divide 360 evenly, so we cannot fit an integral number of decagons around a point (two is too few, and three is too many).
2. Answers will vary.
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6. The eight possibilities for three symbols in a row are , , , , , , , and . (Notice how they can all be listed systematically in terms of alphabetical order.) is not possible (three s in a row), and neither are , , or (two s in a row). is also eliminated because it cannot follow (three s in a row). That leaves , , and ; in a musical sequence, it is that, in fact, occurs after .