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प्रश्न
Is it possible to have a regular polygon whose interior angle is: 155°
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उत्तर
No. of. sides = n
Each interior angle = 155°
∴ `(("2n" - 4) xx 90^circ)/"n" = 155^circ`
180n - 360° = 155n
180n - 155n = 360°
25n = 360°
n = `(360°)/(25°)`
n = `72^circ/5`
Which is not a whole number.
Hence, it is not possible to have a regular polygon whose interior angle is 155°.
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: 160°
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
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 sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of 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.
If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
If each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
Which formula correctly represents the sum of interior angles of an n-sided polygon?
