Analyzing the Problem:

The question involves calculating the angles $a$ and $b$ in a configuration of four regular polygons. Let's solve it step by step:

Key Information:

1. Regular polygons are equiangular and equilateral.
2. The interior angle of a regular polygon with $n$ sides is given by: $\text{Interior Angle} = \frac{(n-2) \cdot 180^\circ}{n}$
3. The polygons are arranged such that their edges and vertices meet.

(a) Calculate the size of angle $a$:

The angle $a$ is formed at the intersection of two polygons' sides. To determine $a$:

• Identify the polygons involved in the diagram.
• Consider how the angles of the polygons contribute at the vertex.

(b) Calculate the size of angle $b$:

Angle $b$ is likely a reflection of the geometry formed by the interaction of the polygons. We will apply the angles of the polygons and the geometry of their connections.

Let me solve this explicitly now.