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प्रश्न
How many sides does a regular polygon have if each of its interior angles is 165°?
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उत्तर
Measure of each interior angle = 165°
Measure of each exterior angle = 180° − 165° = 15°
The sum of all exterior angles of any polygon is 360º.
Thus, number of sides of the polygon = `360^circ/15^circ = 24^circ`
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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The sum of angles of a concave quadrilateral is ______.
The measure of each exterior angle of a regular pentagon is ______.
The number of diagonals in a hexagon is ______.
is a concave pentagon.
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