Axioms of geometry 4

The red angle is always of the same size as the orange angle.

The red angle is always of the same size as the blue angle.

The orange angle is always of the same size as the purple angle.

The purple angle is always of the same size as the purple angle.

The red angle and the orange angle always add up to half a turn.

The red angle and the blue angle always add up to half a turn.

The blue angle and the orange angle always add up to half a turn.

The purple angle and the orange angle always add up to half a turn.