running fixes

The sum of angles in a triangle is 180°

construction 180 degrees total

Let line DAE be parallel to line BC, then the angles a and b equal angles DAB and EAC, respectively. Therefore, the sum of angles in the triangle is 180° : a straight line.
 

"Doubling the angle" yields two equal angles

If 2 * Alpha = Beta than Gamma = Alpha.

a = 30° , b = 60°
thus g = 30°

So, a + d + g = 180°
a + 180 - b + g = 180°
2a = b
a + 180 - 2a + g = 180°
180° - a + g = 180°
-a + g = 0
g = a
 

Two equal angles render an triangle isosceles

isosceles triangle if two angles are equal In the triangle on the right, a = g and b = 2a.
By constructing the bisector (h) of angle b we create two little triangles in which x=y.
Therefore, d1=d2.