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प्रश्न
The number of sides of a regular polygon whose each interior angle is of 135° is ______.
विकल्प
6
7
8
9
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उत्तर
The number of sides of a regular polygon whose each interior angle is of 135° is 8.
Explanation:
We know that, the measures of each exterior angle of a polygon having n sides is given by `360^circ/n`.
∴ The number of sides,
`n = 360^circ/"Exterior angle"`
= `360^circ/(180^circ - 135^circ)` ...[∵ Exterior angle + Interior angle = 180°]
= `360^circ/45^circ`
= 8
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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
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