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