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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°.
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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: 160°
Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle
Is it possible to have a regular polygon whose interior angle is : 170°
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :
(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) 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.
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
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.
Find the number of sides in a regular polygon, if its interior angle is: 150°
