Mathematics Question and Solution
Calculating the interior angles.
It the interior angles be a, b and c identifying them clockwise.
Notice.
The plane shape consist of two composite regular nonagon.
It implies;
d = ⅑(180(9-2))
d = 140°
d is a single interior angle of the composite regular nonagon.
Calculating a.
a = 180-40
a = 40°
Let the side length of the composite regular nonagon be 1 unit.
e² = 1²+1²-2*1*1cos100
e = 1.5320888862 units.
f² = 1.5320888862²+1²-2*1.5320888862*1cos100
f = 1.969615506 units.
Calculating b.
(1.969615506/sin100) = (1/sinb)
b = asin(sin100/1.969615506)
b = 30°
Calculating c.
g = 1+e
g = 1+1.5320888862
g = 2.5320888862 units.
h = 180-30-100
h = 50°
i = 140-50-½(360-140-140)
i = 140-50-40
i = 50°
It implies, angle c is;
c+2i = 180
c = 180-2i
c = 180-2(50)
c = 180-100
c = 80°
Therefore, the required angles in clockwise direction are;
a = 40°
b = 30°
c = 80°
