We know that the sum of the interior angles of a polygon = (n – 2) π
And each angle of polygon = \(\frac{sum\,of\,\,interior\,angles\,of\,polygon}{number\,of\,sides}\)
(i) Pentagon
Number of sides in pentagon = 5
Sum of interior angles of pentagon = (5 – 2) π = 3π
∴ Each angle of pentagon = \(\frac{3π}5\times\frac{180°}π\) = 108°
(ii) Octagon
Number of sides in octagon = 8
Sum of interior angles of octagon = (8 – 2) π = 6π
∴ Each angle of octagon = \(\frac{6π}8\times\frac{180°}π\) = 135°
(iii) Heptagon
Number of sides in heptagon = 7
Sum of interior angles of heptagon = (7 – 2) π = 5π
∴ Each angle of heptagon = \(\frac{5π}7\times\frac{180°}π\) = \(\frac{900}7°\) = 128°34'17"
(iv) Duodecagon
Number of sides in duodecagon = 12
Sum of interior angles of duodecagon = (12 – 2) π = 10π
∴ Each angle of duodecagon = \(\frac{10π}{12}\times\frac{180°}π\) = 150°
