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प्रश्न
Find the number of side of a regular polygon, when of its angle has a measure of 135° .
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उत्तर
\[\text{ Each interior angle }= \left( \frac{2n - 4}{n} \times 90 \right)^° \]
\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 135° \]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{135° }{90° }\]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{3}{2}\]
\[ \Rightarrow 4n - 8 = 3n\]
\[ \therefore n = 8\]
संबंधित प्रश्न
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
| Figure |  |
 |
 |
 |
| Side | 3 | 4 | 5 | 6 |
| Angle sum | 180° |
2 × 180° = (4 − 2) × 180° |
3 × 180° = (5 − 2) × 180° |
4 × 180° = (6 − 2) × 180° |
What can you say about the angle sum of a convex polygon with number of sides?
a) 7
b) 8
c) 10
d) n
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