Mathematics Question and Solution
Let the regular pentagon side length be 1 unit.
Single interior angle of the regular pentagon is;
⅕(180*3)
= 108°
a = 108-90
a = 18°
b = 180-18-108
b = 54°
(1/sin54) = c/sin108)
c = 1.17557050458 units.
d = 108-36
d = 72°
tan72 =e/0.5
e = 1.53884176859 units.
f = 54-18
f = 36°
g² = 1.53884176859²+1.17557050458²-2*1.17557050458*1.53884176859cos36
g = 0.9071653746 units.
(0.9071653746/sin36) = (1.17557050458/sinh)
h = 49.61382244038°
j² = 1+1.53884176859²-2*1.53884176859cos54
j = 1.24860602048 units.
(1.24860602048/sin54) = (1/sink)
k = 40.38617755913°
Therefore, the required angle ? is;
h + k
= 49.61382244038+40.38617755913
= Right-angled.😁😁
