Find the number of sides of a regular polygon whose each exterior angle measures:

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 $=\frac{360}{30}=12$

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