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प्रश्न
Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
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°____ |
Find the number of sides in a regular polygon, if its interior angle is: 160°
Is it possible to have a regular polygon whose interior angle is : 170°
Is it possible to have a regular polygon whose interior angle is:
138°
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.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
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.
Find a number of side in a regular polygon, if it exterior angle is: 30°.
Find number of side in a regular polygon, if it exterior angle is: 36
