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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°____ |
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138°
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(ii) its each exterior angle
(iii) the number of sides in the polygon.
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Which formula correctly represents the sum of interior angles of an n-sided polygon?
