What is the smallest degree of rotation that will map a regular 18 gon on to itself
1 answer:
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Answer: Choice A) 66 degrees
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Minor arc AB (marked in red in the attached diagram) is 45 degrees
Minor arc BE (marked in blue in the same diagram) is 87 degrees
Add the two arcs: 45+87 = 132
Then cut this value in half to get the inscribed angle ADE
132/2 = 66
We cut it in half due to the inscribed angle theorem
Notice how angle ADE cuts off arc ABE (which is composed of minor arc AB and and minor arc BE)
========================================================
Minor arc AB (marked in red in the attached diagram) is 45 degrees
Minor arc BE (marked in blue in the same diagram) is 87 degrees
Add the two arcs: 45+87 = 132
Then cut this value in half to get the inscribed angle ADE
132/2 = 66
We cut it in half due to the inscribed angle theorem
Notice how angle ADE cuts off arc ABE (which is composed of minor arc AB and and minor arc BE)