SOLUTION: What is the number of sides in a regular polygon if the interior angle is 174 degrees?

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Question 266511: What is the number of sides in a regular polygon if the interior angle is 174 degrees?
Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!
the sum of the interior angles of a n sided polygon is given by
sum=180(n-2) degrees
if it is a regular polygon all the sides will be equal in length and so are the angles.
here it is given that the interior angle is 174 degrees
let the number of sides be = n
sum of all the interior angles will be 174*n
but this is equal to 180(n-2)
so 174n=180(n-2)
=> 174n=180n-360
=>6n=360
so n=60
thus number of sides in the polygon = 60 Answer