Advertisements
Advertisements
प्रश्न
Two alternate sides of a regular polygon, when produced, meet at the right angle. Calculate the number of sides in the polygon.
उत्तर
Let number of sides of regular polygon = n
AB & DC when produced meet at P such that
∠P = 90°
∵ Interior angles are equal.
∴ ∠ABC = ∠BCD
∴ 180° - ∠ABC = 180° - ∠BCD
∴ ∠PBC = ∠BCP
But ∠P = 90° (given)
∴ ∠PBC + ∠BCP = 180° - 90° = 90°
∴ ∠PBC =∠BCP
`= 1/2 XX 90° = 45°`
∴ Each exterior angle = 45°
`therefore 45^circ = 360^circ/"n"`
n = `360^circ/45^circ`
n = 8
APPEARS IN
संबंधित प्रश्न
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 interior angle is : 170°
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
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.
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
If the difference between the exterior angle of a 'n' sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
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 number of side in a regular polygon, if it exterior angle is: 36
Is it possible to have a regular polygon whose exterior angle is: 36°
