Final answer:
The swing set and rock climbing area forming a linear pair of congruent adjacent angles would each measure 90 degrees, making two right angles.
Step-by-step explanation:
When two angles form a linear pair, they are adjacent (share a common side) and their non-common sides form a straight line. This is significant in geometry as it implies that the two angles together make a straight angle, which measures 180 degrees. Now, if the city wants to add a swing set and a rock climbing area at angles that are a linear pair and are congruent, each angle would measure half of a straight angle. Congruent means that they are equal in measure, therefore each angle would be 90 degrees because 180 degrees divided by 2 equals 90 degrees.
This concept can be related to a pendulum or a swing set in motion, where the potential and kinetic energy at the peak of the swing would be at a maximum and minimum respectively and inversely at the lowest point of the swing. The same principle of angles applies when considering the tension in wires or ropes, like in the case of a tightrope walker, where equal angles lead to equal tensions.
Therefore, we can determine that the swing set and the rock climbing area would each form a 90-degree angle with the ground, shaping two right angles.