My previous post on Medium introduced a new type of Golden Triangle based on its three angles in proportion to the Golden Ratio. So, once we know that a triangle exists with its angles in Φ or phi proportion (the Golden Ratio, approximately 1.61803…), a logical question to ask is: Can we create other polygons with angles in Φ proportion? The answer is YES!
I should say first that there are other figures called Golden Quadrilaterals, all based on lengths of sides and diagonals in some phi ratio such as a Golden Trapezoid, a Golden Rhombus, a Golden Parallelogram, and a Golden Kite.
Any quadrilateral has angles totaling 360°. We can expand the formula we used to find the three angles of a triangle to search for four angles. That formula is