Mathematics Question and Solution
Calculating the required angle, let it be x.
Let 1 unit be the side length of the both congruent inscribed equilateral triangles.
a = ⅑*180(9-2)
a = 140°
a is the single interior angle of the regular nonagon.
b = ½(a)
b = 70°
c = 180-2b
c = 40°
d² = 2-2cos40
d = 0.68404028665 units.
d is the side length of the regular ascribed nonagon.
e = 60+70
e = 130°
f² = 1²+0.68404028665²-2*1*0.68404028665cos130°
f = 1.53208888624 units.
(1.53208888624/sin130) = (1/sing)
g = asin(0.5)
g = 30°
h = a-g
h = 110°
j² = 1.53208888624²+0.68404028665²-2*0.68404028665*1.53208888624cos110
j = 1.87938524157 units.
Calculating x, the required angle.
(1.87938524157/sin110) = (1.53208888624/sinx)
sinx = 0.76604444312
x = asin(0.76604444312)
x = 50°
