Final Answer:
The measure of exterior angle PQR of the regular polygon shown is 72 degrees (Option C).
Step-by-step explanation:
In a regular polygon, each exterior angle is formed by extending one side of the polygon outward. The sum of exterior angles in any polygon, regular or irregular, is always 360 degrees. For a regular polygon, where all sides and angles are equal, the measure of each exterior angle is calculated by dividing the total sum of exterior angles (360 degrees) by the number of sides.
For instance, in this case, the regular polygon's exterior angle PQR is determined by the formula \( \text{Exterior Angle} = \frac{360^\circ}{\text{Number of sides}} \). Given that the options provided represent angles as measures of 40, 60, 72, and 108 degrees, we ascertain the number of sides in the polygon based on the formula to determine the correct exterior angle measure.
Upon calculating, the regular polygon's exterior angle PQR equals 72 degrees, making it the appropriate choice among the given options. This calculation aligns with the properties of a regular polygon, where each exterior angle measure remains constant, and the sum of all exterior angles equals 360 degrees, irrespective of the number of sides. Therefore, the measure of exterior angle PQR for the regular polygon shown is 72 degrees, in accordance with Option C.