In previous post, I have provided a solution for the problem by triangle area formula, however it seen complicated.
Recently, I have thought up a new solution for it.
Consider the triangle in Cartesian coordinate system, using linear equation for developing the equations for lines AB, AD, CE and BC.
First, assume length of AC is 1
line AB: y = x tan (80)
line AD: y = x tan (60)
line CE: y = x tan (110) - tan (110)
line BC: y = x tan (100) - tan (100)
Point E is intersection of lines AB and CE;
x tan (80) = x tan (110) - tan (110)
x tan (80) - x tan (110) = - tan (110)
x tan (110) - x tan (80) = tan (110)
x [tan (110) - tan (80)] = tan (110)
x = tan (110) / [tan (110) - tan (80)]
x = 0.32635
using line AB equation;
y = 0.32635 tan (80)
y = 1.8508
Point E is (0.32635, 1.85083)
With same method; find for coordinate of D
Point D is (0.766044,1.32683)
Then, find slope of DE by two points;
The slope DE = -1.191753
tan (d) = -1.191753
d = -50 degree or 50 degree
Angle of line EC to horizontal is 70 degree
Then angle e is 70 - 50
thus, answer e = 20 degree
