1. **State the problem:** (a) Find the number of sides of a regular polygon if each exterior angle is 15°. (b) Given three identical regular pentagons arranged with angle $y$ formed between sides of two adjacent pentagons, find the value of $y$. 2. **Formula for exterior angles:** The sum of exterior angles of any polygon is always 360°. Each exterior angle of a regular polygon is given by: $$\text{exterior angle} = \frac{360^\circ}{n}$$ where $n$ is the number of sides. 3. **Part (a) solution:** Given exterior angle = 15°, solve for $n$: $$n = \frac{360^\circ}{15^\circ} = 24$$ So, the polygon has 24 sides. 4. **Part (b) explanation:** Each regular pentagon has interior angles of: $$\text{interior angle} = \frac{(5-2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ$$ 5. **Finding angle $y$ between two adjacent pentagons:** When two pentagons share a vertex, the angle $y$ formed between one side of each pentagon is the exterior angle of the pentagon: $$y = 180^\circ - 108^\circ = 72^\circ$$ 6. **Final answers:** (a) Number of sides = 24 (b) Angle $y = 72^\circ$