No, it appears that you are confused between an axiom and a theorem. An axiom is a self-evident truth, whereas a theorem requires a chain of reasoning. (Oxford Dictionary)
Yes, axioms are self-evident truths. Theorems are true statements derived from axioms (you got that right).
If you were sharp, you would realise that modus ponens, axioms and theorems can be used to make this:
If three-sided figure on Euclidean plane (axiom), then interior angles always add up to half a rotation (theorem).
Given three-sided figure on Euclidean plane.
Therefore interior angles add up to half a rotation.
Or to put it differently:
If axiom P, then theorem Q is true
Axiom P is given,
Therefore theorem Q is true.
At last you got the difference between an axiom and a theorem right! I’m glad to have been of assistance. Now all you need to realize is that you cannot prove the validity of a theorem with a modus ponens. It is quite irrelevant to the argument.