Mathematics Question and Solution
Let the three equal lengths of the ascribed pentagon be 1 unit each.
a² = 2-2cos80
a = 1.2855752194 units.
b = ½(180-80)
b = 50°
c = 80-b
c = 30°
d = 90-b
d = 40°
It implies;
(1.2855752194/sine) = (1/sin30)
e = 40°
30+40+40+f = 180
f = 180-110
f = 70°
g = 180-70-80
g = 30°
(1/sin30) = (h/sin70)
h = 1.8793852416 units.
j² = 1+1.2855752194²-2*1.2855752194cos(70+40)
j = 1.8793852416 units.
Notice;
h = j
It implies;
k = ½(180-(80-40))
k = ½(180-40)
k = 70°
Therefore, the required angle ? is;
?+30 = 70
? = 70-30
? = 40°
