Which branch of the government has often been charged with interpreting the proper extent of presidential powers? give 1 example

The Judicial Branch

The Judicial Branch, as a guardian and interpreter of the laws stated in the Constitution, often has the responsibility to interpret the proper extension of the other branches, including the presidential powers, as well as to tell if the president violates a law based on the Constitution.

Example: Let's suppose the President decides to declare war on a country and spread it to media. The Judicial branch is the one to formally denounce that his actions are unconstitutional since it is the Legislative Branch's responsibility of doing so.