Advertisements
Advertisements
प्रश्न
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.
उत्तर
∵ Polygon is regular (Given)
∴ AB = BC
⇒ ∠BAC = ∠BCA ...[∠S opposite to equal sides]
But ∠BAC = 20°
∴ ∠BCA = 20°
i.e. In Δ ABC,
∠B + ∠BAC + ∠BCA = 180°
∠B + 20° + 20° = 180°
∠B = 180° - 40°
∠B = 140°
(i) each interior angle = 140°
(ii) each exterior angle = 180°- 140°= 40°
(iii) Let no. of. sides = n
`therefore 360^circ/"n" = 40^circ`
n = `360^circ/40^circ = 9`
n = 9
APPEARS IN
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: 160°
Find the number of sides in a regular polygon, if its exterior angle is : `1/3` of right angle
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.
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 interior angle is: 135°
Is it possible to have a regular polygon whose exterior angle is: 100°
Is it possible to have a regular polygon whose exterior angle is: 36°
