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.

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(53765) (Show Source): You can put this solution on YOUR website!
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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 = = 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�.

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