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

Question 266511: What is the number of sides in a regular polygon if the interior angle is 174 degrees?
Answer by vksarvepalli(154) (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
RELATED QUESTIONS
Each interior angle of a regular polygon is 174 degrees. Work out the number of sides... (answered by Alan3354)

each interior of a regular polygon is 174 degrees what is each exterior angle? how many... (answered by Earlsdon,JimboP1977)

If each exterior angle of a regular polygon is 30 degrees , find an interior angle and... (answered by Alan3354)

If one interior angle of a regular polygon is 157.5. What is the number of sides of the... (answered by Alan3354)

A regular polygon has 14 sides what is the degrees of each interior... (answered by Cromlix)

Find the number of sides of a regular polygon if one interior angle is 60 degrees.... (answered by Alan3354)

Find the number of sides of a regular polygon if one interior angle is 120 degrees.... (answered by htmentor)

The exterior angle of a regular polygon is 100 degrees less than the interior angle. What (answered by Alan3354)

Find the number of sides of a regular polygon if one interior angles is 60... (answered by ikleyn)