Mathematics Question and Solution
Let the side length of the regular pentagon be 1 unit.
a² = 2-2cos108
108° is the single interior angle of the regular pentagon.
a = 1.6180339887 units.
a is BE.
b = 108-60
b = 48°
c = ½(180-48)
c = 66°
d = 180-60-c
d = 54°
e = 180-d-b
e = 78°
f = 180-e
f = 102°
g = 180-f-72
g = 6°
g is angle BEG = angle BGE.
h = 180-2g
h = 168°
h is angle EBG.
j = h-72
j = 96°
j is angle CBG.
k = a-1
k = 1.6180339887-1
k = 0.6180339887 units..
k is BF
l² = 0.6180339887²+1-2*0.6180339887cos96
l = 1.2292966678 units.
l is CF.
Therefore, the required angle alpha is;
Let it be m.
(0.6180339887/sinm) = (1.2292966678/sin96)
m = asin(0.5)
m = 30°
Therefore,
Alpha = m = 30°
