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Question
Find the number of side of a regular polygon, when of its angle has a measure of 135° .
Solution
\[\text{ Each interior angle }= \left( \frac{2n - 4}{n} \times 90 \right)^° \]
\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 135° \]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{135° }{90° }\]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{3}{2}\]
\[ \Rightarrow 4n - 8 = 3n\]
\[ \therefore n = 8\]
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