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प्रश्न
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
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उत्तर
Let interior angle = x
Then exterior angle = x + 60
∴ x + x + 60° = 180°
⇒ 2x = 180° - 60° = 120°
⇒ x = `(120°)/2 = 60°`
∴ Exterior angle = 60° + 60° = 120°
∴ Number of sides = `(360°)/(120°) = 3`
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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
Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle
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°
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°
Is it possible to have a regular polygon whose interior angle is: 135°
Which formula correctly represents the sum of interior angles of an n-sided polygon?
