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प्रश्न
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
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उत्तर
Let interior angle = x°
Exterior angle =`1/3` x°
`therefore "x" + 1/3 "x" = 180^circ`
3x + x = 540
4x = 540
x = `540/4`
x = 135°
∴ Exterior angle = `1/3 xx 135^circ = 45^circ`
Let no.of. sides = n
∵ each exterior angle = `360^circ/"n"`
∴ 45° = `(360°)/"n"`
∴ n = `(360°)/(45°)`
n = 8
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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: `1 1/5` of a right angle
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°
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
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.
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 each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
Which formula correctly represents the sum of interior angles of an n-sided polygon?
