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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.
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: 160°
Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle
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.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
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.
Find a number of side in a regular polygon, if it exterior angle is: 30°.
Find number of side in a regular polygon, if it exterior angle is: 36
Is it possible to have a regular polygon whose interior angle is: 135°
