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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°____ |
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Is it possible to have a regular polygon whose interior angle is:
138°
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.
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(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
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Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
Is it possible to have a regular polygon whose interior angle is: 155°
What is the sum of all exterior angles of any regular polygon?
