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प्रश्न
Find the number of side of a regular polygon, when of its angle has a measure of 162° .
उत्तर
\[ \text{ Each interior angle } = \left( \frac{2n - 4}{n} \times 90 \right)^° \]
\[So, \left( \frac{2n - 4}{n} \times 90 \right)^° = 162° \]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{162° }{90° }\]
\[ \Rightarrow \frac{2n - 4}{n} = \frac{9}{5}\]
\[ \Rightarrow 10n - 20 = 9n\]
\[ \therefore n = 20\]
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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
d) n
What is a regular polygon?
Classify the following curve as open or closed:
Find the number of side of a regular polygon, when of its angle has a measure of 160° .
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A nonagon has ______ sides.
is a polygon.
If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.
A polygon is regular if all of its sides are equal.
A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find ∠BCF.
