This brilliant task shared by Stephen Gregory (@ALPMaths) feels like the spiritual successor to Sam Blatherwick‘s wonderful task Using Ratios to Find Angles.

I really like having these different ways to interweave sharing ratios into different topics. It is such a key skill and it is nice to see it applied in so many different ways. This task, in particular, brings in some nice properties of different ‘special’ quadrilaterals and, of course, sums of interior angles in polygons.