SOLUTION: What is the vertex defect at a vertex where an equilateral triangle, a square and a regular pentagon meet? What is the answer in degrees and as a fraction.

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Question 1000354: What is the vertex defect at a vertex where an equilateral triangle, a square and a regular pentagon meet? What is the answer in degrees and as a fraction.
Answer by ikleyn(53763) About Me  (Show Source):
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What is the vertex defect at a vertex where an equilateral triangle, a square and a regular pentagon meet? What is the answer in degrees and as a fraction.
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An equilateral triangle contributes  60°.

A square contributes  90°.

A regular pentagon contributes  180%2A%28n-2%29%2F5 = 180%2A%285-2%29%2F5 = 108°.

The sum of these angles is  60° + 90° + 108° = 258°.

A vertex defect  (see  this article  from Wikipedia)  is the difference between  360°  and this sum,  i.e.  360° - 258° = 102°.