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प्रश्न
Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
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उत्तर
Let number of sides of a regular polygon = n
Let exterior angle = x
Then interior angle = 5x
x + 5x = 180°
⇒ 6x = 180°
⇒ x = `180^circ/6 = 30^circ`
∴ Number of sides (n) = `(360°)/30 = 12`
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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°____ |
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
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 exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
Find a number of side in a regular polygon, if it exterior angle is: 30°.
Is it possible to have a regular polygon whose interior angle is: 155°
Which formula correctly represents the sum of interior angles of an n-sided polygon?
