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प्रश्न
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
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उत्तर
Let interior angle = x°
Exterior angle =`1/3` x°
`therefore "x" + 1/3 "x" = 180^circ`
3x + x = 540
4x = 540
x = `540/4`
x = 135°
∴ Exterior angle = `1/3 xx 135^circ = 45^circ`
Let no.of. sides = n
∵ each exterior angle = `360^circ/"n"`
∴ 45° = `(360°)/"n"`
∴ n = `(360°)/(45°)`
n = 8
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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 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.
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.
Find the number of sides in a regular polygon, if its interior angle is: 150°
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: 36°
What is the measure of each interior angle of a regular hexagon?
A regular polygon has each exterior angle measuring 40°. How many sides does it have?
