Question

Find the number of side of a regular polygon, when of its angle has a measure of 175° .

Answer 1

\[ \text{ Each interior angle } = \left( \frac{2n - 4}{n} \times 90 \right)^° \]

\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 175° \]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{175° }{90° }\]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{35}{18}\]

\[ \Rightarrow 36n - 72 = 35n\]

\[ \therefore n = 72\]