Final answer:
The common pressure angles used in gear design today are 14.5 degrees and 20 degrees, which are crucial in determining gear teeth shape and system efficiency.
Step-by-step explanation:
The two common pressure angles that are typically found in gear design today are 14.5 degrees and 20 degrees. These pressure angles are important as they directly relate to the shape and strength of the gear teeth, influencing the operation and efficiency of the gear system. The two options provided that represent these common pressure angles are additionally labeled as 20 degrees and 25 degrees, 25 degrees and 30 degrees, and 30 degrees and 35 degrees; however, these are less common in practice compared to the 14.5 degrees and 20 degrees standards. Understanding these angles is crucial for engineers and designers when creating gears for various mechanical applications.