Advertisements
Advertisements
प्रश्न
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.
उत्तर
Interior angle : exterior angle = 2 : 1
Let interior angle = 2x° & exterior angle = x°
∴ 2x° + x° = 180°
3x = 180°
x = 60°
∴ Each exterior angle = 60°
Let no.of. sides = n
`(360°)/"n" = 60°`
n = `(360°)/(60°)`
n = 6
∴ (i) x = 60° (ii) 6
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: 135°
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.
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.
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in 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.
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.
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.
Calculate the number of sides of a regular polygon, if: its interior angle is five times its exterior angle.
Calculate the number of sides of a regular polygon, if: the ratio between its exterior angle and interior angle is 2: 7.
Calculate the number of sides of a regular polygon, if: its exterior angle exceeds its interior angle by 60°.
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
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 interior angle is: 135°
Is it possible to have a regular polygon whose interior angle is: 155°
Is it possible to have a regular polygon whose exterior angle is: 100°
