I'm trying to prove $$\text {If}\ \angle P \lt \angle Q, \text & \ \angle Q \cong \angle R, \text{Then}\ \angle P \lt \angle R$$Which seems super basic and makes sense, but I got told that I'm under thinking the proof and that I need to think triangle congruences to get angle congruences to show the less than/ greater than.
Anyone got any advice for me?
Edit:
The down votes would be better had there also been a comment as to why. If you'd like me to prove that I've put effort into this problem already I could put up my work for the part right before this question where I proved, i think, that trichotomy holds with two angles P and Q. I'm just having more trouble on these angles then I did on the segments in the previous questions.
What it might be, is the fact that you left out measures. Be specific in proofs, instead of $\angle P < Q$, use $m\angle P < m\angle Q$, if two angles have equal measures, then they are congruent. Therefore $\angle P$ is congruent to $\angle Q$, and since $\angle Q$ is congruent to $\angle R$, by transitive property of inequality, $\angle P$ is congruent to $\angle R$.
Don't forget when you're saying one angle is greater or less than another angle, it is important that you don't just address the angles, but the measure of the angles. And this proof uses transitive property of inequality. Hopefully this helps. Peace!