Question

Find the number of side of a regular polygon, when of its angle has a measure of 160° .

Answer 1

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

\[So, \left( \frac{2n - 4}{n} \times 90 \right)^°  = 160°  \]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{160°  }{90° }\]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{16}{9}\]

\[ \Rightarrow 18n - 36 = 16n\]

\[ \Rightarrow 2n = 36\]

\[ \therefore n = 18\]