Question

find the number of side of a regular polygon if each of its interior angle is .
(I). 90. (ii) 108. (iii). 165​

Answer 1

Answer:

(a) 4 sides

(b) 5 sides

(c) 24 sides

Explanation:

(a) (n-2)180⁰=90⁰n

180⁰n-360⁰=90⁰n

180⁰n-90⁰n=360⁰

90⁰n=360⁰

n=360⁰/90⁰

n=4

(b) (n-2)180⁰=108⁰n

180⁰n-360⁰=108⁰n

180⁰n-108⁰n=360⁰

72⁰n=360⁰

n=360⁰/72⁰

n=5

(c) (n-2)180⁰=360⁰n

180⁰n-360⁰=165⁰n

180⁰n-165⁰n=360⁰

15⁰n=360⁰

n=360⁰/15⁰

n=24