Question:
Find the number of sides of a regular polygon whose each exterior angle measures:
(i) 40°
(ii) 36°
(iii) 72°
(iv) 30°
Solution:
Sum of all the exterior angles of a regular polygon is $360^{\circ}$.
(i) Each exterior angle $=40^{\circ}$
Number of sides of the regular polygon $=\frac{360}{40}=9$
(ii) Each exterior angle $=36^{\circ}$
Number of sides of the regular polygon $=\frac{360}{36}=10$
(iii) Each exterior angle $=72^{\circ}$
Number of sides of the regular polygon $=\frac{360}{72}=5$
(iv) Each exterior angle $=30^{\circ}$
Number of sides of the regular polygon $=\frac{360}{30}=12$