Each interior angle of a regular polygon is equal to 172 degrees. Determine the number of sides of the polygon. Explain?

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Each interior angle of a regular polygon is equal to 172 degrees. Determine the number of sides of the polygon. Explain?

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Answer 1 · 2016-05-15T23:13:24

#45# sides

Explanation:

A regular polygon with #n# sides has a total of #(n-2)180^o# internal degrees. This can be understood as the number of triangles in which the polygon can be decomposed.
A regular polygon with an interior angle of #172^o# has a total of
#n 172^o#. So we have
#n 172 = (n-2)180#. Solving for #n# we have #n = 45#

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Each interior angle of a regular polygon is equal to 172 degrees. Determine the number of sides of the polygon. Explain?

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