Mathematics Question and Solution
Calculating x, the required angle.
Let the side length of the regular pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b² = 1²+0.5²-2*1*0.5cos108
b = 1.24860602048 units.
(1.24860602048/sin108) = (1/sinc)
c = 49.6138224406°
d = 180-108-c
d = 72-49.6138224406
d = 22.3861775594°
e = 180-c-d
e = 180-49.6138224406-22.3861775594
e = 108°
e = a.
(0.5/sin108) = (f/sin49.6138224406)
f = 0.40044657145 units.
g = b-f
g = 1.24860602048-0.40044657145
g = 0.84815944903 units.
h = 180-c
h = 180-49.6138224406
h = 130.386177559°
j² = 0.5²+0.84815944903²-2*0.5*0.84815944903cos130.386177559
j = 1.2324478205 units.
(1.2324478205/sin130.386177559) = (0.5/sink)
k = asin(0.30901699437)
k = 18°
It implies, the required angle x is;
x+k = a = e
x+18 = 108
x = 108-18
x = 90°
