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Question
Find the number of side of a regular polygon, when of its angle has a measure of 175° .
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Solution
\[ \text{ Each interior angle } = \left( \frac{2n - 4}{n} \times 90 \right)^° \]
\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 175° \]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{175° }{90° }\]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{35}{18}\]
\[ \Rightarrow 36n - 72 = 35n\]
\[ \therefore n = 72\]
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