Question:
The number of sides of a regular polygon whose each interior angle is of 135o is
(a) 6
(b) 7
(c) 8
(d) 9
Solution:
Now let us assume number of sides of a regular polygon be n.
WKT, sum of all exterior angles of all polygons is equal to 360o.
Form the question it is given that each exterior angle has a measure of 45o.
Then,
n = 360o/Exterior angle
n = 360o/(180o – 135o)
n = 360o/45o
n = 8