What program can I observe the angles between the lines of the robotic arm?

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lines? angles? do you mean the angle between the parts of the arms?

please explain more clearly...

yes exactly that's what i want. and get cartesian position from joint angles

Well, there is most probably tf which let's you observe the rotations between coordinate systems, or the joint_states topic on which you can see the states of the joints of your robot arm. This should probably work as you are mentioning moveit. Though you might have to compensate for some static offsets.

Then again, this is depending on how the robot arm is modeled and without more information about what type you are using, we cannot provide more help here.

get cartesian position from joint angles

cartesion position of what? again, tf should be your friend here...