Solution:
This is known that the sum of the interior angles of a polygon is equal to (n – 2) π, where n represents the number of sides in the given polygon.
Each angle of a polygon is equal to the sum of the interior angles of the polygon/number of sides.
(i) Pentagon
We know that there are 5 sides to the pentagon. Therefore n = 5
Using the above relation, the sum of interior angles of the pentagon is given by:
(5 – 2) π = 3π
Therefore, each angle of pentagon is:
= 3π/5 × 180o/ π
= 108o
(ii) Octagon
Similarly, there are 8 sides to an octagon
Therefore, the sum of interior angles of the octagon is given by:
= (8 – 2) π
= 6π
Thus, each angle of the octagon is:
= 6π/8 × 180o/ π
= 135o