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

(i) Pentagon (ii) Octagon (iii) Heptagon (iv) Duodecagon.

We know that the sum of the interior angles of a polygon = (n – 2) π


And each angle of polygon


(i) Pentagon


Number of sides in pentagon = 5


Sum of interior angles of pentagon = (5 – 2) π = 3π


Each angle of pentagon


(ii) Octagon


Number of sides in octagon = 8


Sum of interior angles of octagon = (8 – 2) π = 6π


Each angle of octagon


(iii) Heptagon


Number of sides in heptagon = 7


Sum of interior angles of heptagon = (7 – 2) π = 5π


Each angle of heptagon


(iv) Duodecagon


Number of sides in duodecagon = 12


Sum of interior angles of duodecagon = (12 – 2) π = 10π


Each angle of duodecagon


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