Question

When tiles are tessellated in a plane, what angle measure sum is required of the tiles surrounding a single point?

Answer 1

The angle measures must sum to 360 in order for the figure to tessellate about a vertex.

Answer 2

We know from basic geometry that the sum of angles about a point is always $360^{\circ}$. Thus, in our case too this will remain the same and hence the angle will remain $360^{\circ}$.

Therefore, when tiles are tessellated in a plane, the angle measure sum that is required of the tiles surrounding a single point is always $360^{\circ}$.