To tessellate a plane means to cover the plane with flat tiles so that there
are no gaps or overlaps.

It is not the sum of the angles - a hexagon tessellates, but the sum the
angles is more than 360°.

A circle is 360°. Angles around a point have to equal 360°. If you have
tiles on your floor.... imagine you're placing your finger where four
corners come together... the sum of the 4 90° angles is 360°.

You can use pattern blocks to create a radial design and follow the same
logic - but it is not a regular tessellation - or periodic tiling -

Albrecht Durer created a tessellated design using pentagons and rhombi -
dated 15th century.