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Invariant Angle Sets

         

As the base of the purple triangle collapses from 4 units to 1 unit, what happens to the sum of the four red, external angles shown in the diagram?

A regular hexagon on a grid is squashed down 1 unit. What happened to the angle sum of the angles shown in red once the hexagon was changed?

In both images a regular pentagon and a regular hexagon overlap at different points to create a quadrilateral in the center. Which is larger, the sum of the two blue angles or the sum of the two pink angles?

The following image is a map of four color-coded exhibit spaces in a museum. In which of these four polygonal rooms is the sum of the internal angles largest?

If all four of the quadrilaterals below are parallelograms, what is the sum of the four gray angles?

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