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प्रश्न
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
उत्तर
Let exterior angle = x° & interior angle = 4x°
∴ 4x + x = 180°
5x = 180°
x = 36°
∴ Each exterior angle = 36°
Let no.of sides = n
∴ `360^circ/"n" = 36^circ`
n = `360^circ/36^circ`
n = 10
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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°____ |
Find the number of sides in a regular polygon, if its interior angle is: 160°
Is it possible to have a regular polygon whose interior angle is : 170°
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°
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
The difference between the exterior angles of two regular polygons, having the sides equal to (n – 1) and (n + 1) is 9°. Find the value of n.
If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
Find the number of sides in a regular polygon, if its interior angle is: 150°
