Question

Find the number of side of a regular polygon, when of its angle has a measure of 135° .

Answer 1

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

\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 135° \]

\[ \Rightarrow \frac{2n - 4}{n} = \frac{135° }{90° }\]

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

\[ \Rightarrow 4n - 8 = 3n\]

\[ \therefore n = 8\]