Question 266511
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