Mathematics Question and Solution
Calculating the value of alpha(x) ÷ beta(y) (x/y).
Calculating alpha (x).
x = ⅕*180(5-2)
x = ⅕*180*3
x = 108°
Where x is alpha and also the single interior angle of the regular pentagon.
Let 2 units be the side length of the regular pentagon.
a = ½(2)
a = 1 unit.
b² = 1²+2²-2*1*2cos108
b = 2.49721204096 units.
b is the sum of the radius of the inscribed half circle and the radius of the inscribed 108° sector.
(2.49721204096/sin108) = (1/sinc)
c = 22.3861775591°
d = 180-108-c
d = 180-108-22.3861775591
d = 49.6138224409°
f = 180-d
f = 180-49.6138224409
f = 130.386177559°
f' = 0.5(180-f)
f' = 0.5(180-130.386177559)
f' = 24.8069112205°
g = 108-c
g = 108-22.3861775591
g = 85.6138224409°
g' = 0.5(180-g)
g' = 0.5(180-85.6138224409)
g' = 47.1930887796°
It implies, beta (y) is;
180-f'-g'
y = 180-24.8069112205-47.1930887796
y = 108°
y is beta.
Therefore, alpha(x) ÷ beta(y) (x/y) is;
108/108
= 1
