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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: 135°
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
The ratio between the interior angle and the exterior angle of a regular polygon is 2: 1. Find:
(i) each exterior angle of the polygon ;
(ii) number of sides in the polygon.
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.
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.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in 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.
Is it possible to have a regular polygon whose exterior angle is: 100°
If each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
