Here are the steps to the answer with the alternative starting point. In the diagram below, all the colored line segments are the same length, as explained below the diagram.
Legs of a 80-20-80 isosceles triangle
Legs of a 50-80-50 isosceles triangle
Legs of a 40-100-40 isosceles triangle
Sides of an equilateral triangle
So the triangle with one yellow and one blue leg is isosceles, and the angle near the bottom of the diagram is 180-80-60=40, so the triangle is 70-40-70
The angle we want is 70 from the blue-yellow triangle minus 40 from the blue triangle = 30*
Easy, huh? Not so I can tell it!