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प्रश्न
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
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उत्तर
Let each exterior angle or interior angle be = x°
∴ x + x = 180°
2x = 180°
x = 90°
Now, let no. of sides = n
∵ each exterior angle = `360^circ/"n"`
∴ 90° = `360^circ/"n"`
n = `360^circ/90^circ`
n = 4
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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 interior angle is:
138°
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Find a number of side in a regular polygon, if it exterior angle is: 30°.
Is it possible to have a regular polygon whose exterior angle is: 100°
Is it possible to have a regular polygon whose exterior angle is: 36°
Which formula correctly represents the sum of interior angles of an n-sided polygon?
