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.
Advertisements
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 interior angle is: `1 1/5` of a right angle
Is it possible to have a regular polygon whose interior angle is : 170°
Is it possible to have a regular polygon whose interior angle is:
138°
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 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 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.
Is it possible to have a regular polygon whose exterior angle is: 36°
If each interior angle of a regular polygon is 144°, what is its corresponding exterior angle?
