Find the magnitude, in radians and degrees, of the interior angle of aregular(i)pentagon (ii)octagon(iii) heptagon (iv) duodecagon.

Find the magnitude, in radians and degrees, of the interior angle of a

1.	Find the magnitude, in radians and degrees, of the interior angle of aregular(i)pentagon (ii)octagon(iii) heptagon (iv) duodecagon.
Answer» Sum of the interior angles of n-sided polygon is given as `(n-2)pi`. `:.` Interior angle of regular polygon `= ((n-2)pi)/n` (i) Interior angle of regular pentagon `= ((5-2)pi)/5 = (3pi)/5` radians Interior angle in degrees `= 3/5180 = 108^@` (ii) Interior angle of regular octagon`= ((8-2)pi)/8 = (6pi)/8 = (3pi)/4` radians Interior angle in degrees `= 3/4180 = 135^@` (iii) Interior angle of regular heptagon `= ((7-2)pi)/7 = (5pi)/7` radians Interior angle in degrees `= 5/7180 = (900/7) ^@` (iv) Interior angle of regular duodecagon`= ((12-2)pi)/12 = (5pi)/6` radians Interior angle in degrees `= 5/6180 = 150 ^@`