In a regular tiling, if there are six polygons meeting at a vertex, then the angles at the vertex are _______ degrees.
A)45
B)60
C)90
D)120

Question

Quizplus · Accepted Answer

In a regular tiling, all angles and sides of the polygons are congruent. Let's consider the polygons meeting at a vertex. Since there are six polygons meeting at a vertex, they must be hexagons.

Each angle of a regular hexagon measures 120 degrees. At the vertex, we have six such angles, forming a full circle of 360 degrees. Thus, the sum of the angles at the vertex is 6 x 120 = 720 degrees.

Since these angles are evenly distributed around the vertex, they must each measure 720 degrees/6 = 120 degrees. However, this is the external angle of the polygon, and we need to find the interior angle at the vertex.

We know that the exterior and interior angles at any vertex are supplementary, meaning that they add up to 180 degrees. Thus, the interior angle at the vertex is 180 - 120 = 60 degrees. Therefore, the best choice is B) 60.

In a Regular Tiling, If There Are Six Polygons Meeting