Final answer:
The angle between two consecutive radii of a regular hexagon is 60°, and the angle between a radius and a side of the hexagon is 90°.
Step-by-step explanation:
To answer the student's question regarding a regular hexagon and the measure of angles formed by two consecutive radii (a) and the measure of angles formed by a radius and a side of the polygon (b), we need to understand the properties of a regular hexagon. A regular hexagon is a six-sided polygon where all sides and angles are equal.
For part (a), we first recognize that a regular hexagon can be divided into six equilateral triangles by drawing all its radii, which connect the center of the hexagon to its vertices. Since each triangle is equilateral, each angle is 60°. Therefore, the angle between two consecutive radii is also 60°.
For part (b), the angles between a radius and a side of a regular hexagon essentially form a right angle, as the radius to a vertex forms an isosceles triangle on each side of the hexagon. Since a side is tangential to the circumcircle at a polygon's vertex and the radii meet the vertices perpendicularly, the angle formed by a radius and a side of the polygon is 90°.