Mathematics Question and Solution
Let AB = 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
a is AD.
b = 108-36-18
b = 54°
b is angle DAF.
c = 108-36-30
c = 42°
c is angle ADF.
d = 180-54-42
d = 84°
d is angle AFD.
(1.61803398875/sin84) = (e/sin54)
e = 1.31622742593 units.
e is DF.
(CF)² = 1.31622742593+1-2*1.31622742593cos30
CF = 0.6728163648 units.
(0.6728163648/sin30) = (1.31622742593/sinf)
f = 78°
f is the supplementary angle of angle g.
Calculating angle g.
g+f = 180
g = 180-f
g = 180-78
g = 102°
g is angle DCF.
Therefore, the required angle is;
Let it be h.
It implies;
g+h = 108
102+h = 108
h = 108-102
h = 6°
