Question

Find the number of side of a regular polygon, when of its angle has a measure of 150° .

Answer 1

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

\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 150° \]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{150° }{90° }\]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{5}{3}\]

\[ \Rightarrow 6n - 12 = 5n\]

\[ \therefore n = 12\]