Question

Find the number of side of a regular polygon, when of its angle has a measure of 162° .

Answer 1

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

\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 162° \]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{162°  }{90° }\]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{9}{5}\]

\[ \Rightarrow 10n - 20 = 9n\]

\[ \therefore n = 20\]