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प्रश्न
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
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उत्तर
Ratio between exterior angle and interior angle = 2: 7
Let exterior angle = 2x
Then interior angle = 7x
∴ 2x + 7x = 180°
⇒ 9x = 180°
`=> "x" = (180°)/9 = 20°`
∴ Ext. angle = 2x = 2 × 20° = 40°
∴ No. of. sides = `(360°)/40 = 9`
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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: `1 1/5` of a right angle
Find the number of sides in a regular polygon, if its exterior angle is: two-fifth of right angle
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 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 ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in 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.
What is the measure of each interior angle of a regular hexagon?
Which formula correctly represents the sum of interior angles of an n-sided polygon?
