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प्रश्न
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
उत्तर
Let each exterior angle or interior angle be = x°
∴ x + x = 180°
2x = 180°
x = 90°
Now, let no. of sides = n
∵ each exterior angle = `360^circ/"n"`
∴ 90° = `360^circ/"n"`
n = `360^circ/90^circ`
n = 4
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संबंधित प्रश्न
Fill in the blanks :
In case of regular polygon, with :
| No.of.sides | Each exterior angle | Each interior angle |
| (i) ___8___ | _______ | ______ |
| (ii) ___12____ | _______ | ______ |
| (iii) _________ | _____72°_____ | ______ |
| (iv) _________ | _____45°_____ | ______ |
| (v) _________ | __________ | _____150°_____ |
| (vi) ________ | __________ | ______140°____ |
Is it possible to have a regular polygon whose interior angle is:
138°
Is it possible to have a regular polygon whose each exterior angle is: 80°
The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Find the number of sides in a regular polygon, if its interior angle is: 150°
Is it possible to have a regular polygon whose interior angle is: 135°
Is it possible to have a regular polygon whose exterior angle is: 100°
