Mathematics Question and Solution
Calculating angle x.
Notice.
The composite plane shape is not drawn to scale.
Let the three equal lengths be 1 unit each.
It implies;
AB = BD = DE = 1 unit.
Let y be CD.
a = (1+y) units.
a is BC.
Calculating y.
tan15 = 1/a
tan15 = 1/(1+y)
tan15+ytan15 = 1
y = (1-tan15)/(tan15)
y = 2.73205080757 units.
Again, y is CD.
(2.73205080757/sinb) = (1/sin15)
sinb = 2.73205080757sin15
b = asin(0.70710678119)
b = 45°
b is the supplementary angle of angle CED.
c = 180-b
c = 180-45
c = 135°
c is angle CED.
It implies, the required angle x, angle CDE is;
x+15+c = 180
x = 180-15-135
x = 180-150
x = 30°
