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प्रश्न
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.
उत्तर
Let exterior angle = x°
Interior angle = 5x°
x + 5x = 180°
6x = 180°
x = 30°
Each exterior angle = 30°
Each interior angle = 5 x 30° = 150°
Let no. of sides = n
∵ each exterior angle = `360^circ/"n"`
`30^circ = (360^circ)/"n"`
n = `(360^circ)/30^circ`
n = 12
Hence (i) 150° (ii) 30° (iii) 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 exterior angle is : `1/3` of right angle
Is it possible to have a regular polygon whose each exterior angle is: 80°
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.
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.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
Find the number of sides in a regular polygon, if its interior angle is: 150°
Is it possible to have a regular polygon whose interior angle is: 135°
