Mathematics Question and Solution
Let the side length of the regular pentagon be 1 unit.
a = 108-90
a = 18°
108° is the single interior angle of the regular pentagon.
b = 90-18
b = 72°
c =108-72
c = 36°
sin18 = d/1
d = 0.3090169944 units.
e² = 1+0.3090169944²-2*0.3090169944cos36
e = 0.7716809592 units.
(0.7716809592/sin36) = (0.3090169944/sinf)
f = 13.6138224422°
g² = 1²+0.5²-2*0.5cos108
g = 1.2486060205 units.
(1.2486060205/sin108) = (0.5/sinh)
h = 22.3861775592°
j = 108-13.6138224422-h
j = 72°
k² = 1.2486060205²+0.7716809592²-2*1.2486060205*0.7716809592cos72
k = 1.2486060205 units.
It implies;
Since k = g, the required angle x, is;
x = 72°
