Mathematics Question and Solution
Let the regular pentagon side be 1 unit.
a = ⅕(180*3)
a = 108°
a is an angle of the regular pentagon.
b = 108-36
b = 72°
c = 180-45-72
c = 180-117
c = 63°
(d/sin63) = (1/sin45)
d = 1.26007351067 units.
cos72 = e/1
e = 0.30901699437 units.
f = 2e+1
f = 2(0.30901699437)+1
f = 1.61803398875 units.
g = f-d
g = 1.61803398875-1.26007351067
g = 0.35796047808 units.
h² = 0.35796047808²+0.5²-2*0.35796047808*0.5cos36
h = 0.2975560347 units.
Calculating x.
(0.5/sinj) = (0.2975560347/sin36)
sinj = (0.5sin36)/ 0.2975560347
j = 81°
Therefore;
x = 180-j
x = 180-81
x = 99°
