Question

find the number of sides of a regular polygon when each of its angles has measure of 175 degree

Answer 1

72

Step-by-step explanation:

175° = (n-2)x180÷n

175n = 180n - 360

360 = 180n-175n

360 = 5n

180/5 = n

72 = n

Answer 2

Given that interior angle=175°, the number of sides of a regular polygon is 72.

Step-by-step explanation:

• Each Interior angle of the regular polygon =   (n−2)/n  ×180°

•  ⇒  175° =  (n−2)/n ×180°  
• ⇒  175n=180n−360
• ⇒  360=180n−175n
• ⇒  360=5n
• ⇒  n=  360/5

• ​ ∴  n=72

• ∴  Number of sides in the regular polygon is 72.