Mathematics Question and Solution
Calculating angle x.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b = 108-½(180-108)
b = 108-36
b = 72°
c = 90-72
c = 18°
d = 60+108
d = 168°
e = ½(d)
e = ½(168)
e = 84°
f = e-72
f = 84-72
f = 12°
g = 180-c-f
g = 180-18-12
g = 180-30
g = 150°
Let the side length of the regular pentagon be 1 unit.
h² = 2-2cos108
h = 1.6180339887 units.
It implies;
Observing Sine Rule.
(1.6180339887/sin150) = (j/sin18)
j = 1 unit.
k = ½(180-84)
k = ½(96)
k = 48°
Therefore, the required angle x is;
x = 2k
x = 2(48)
x = 96°
