Why are there 2 different ways to measure angles between Radians and Degrees.

It's just like inches and meters.

beause some problems require that you use eithe one or the other of both just like you have to use diffrent methods to solve variables depending on what is needed

Also, there are some calculus problems that you can only do with radians.

Degrees are used for almost all every day uses - eg Latitude and longitude surveying etc