Answer: See attached image and view below.
Step-by-step explanation:
Besides the figure LQNP, we are not given any other information. While we can assume several things, for example, that LQ ║ NP, but this is an assumption. This means we will not start with a given statement. We know that we need to prove that ∠LMQ ≅ ∠PMN.
The first thing I notice is the vertical angles. We can prove the statement ∠LMQ ≅ ∠PMN with the justification of vertical angles. Vertical angles will always be congruent. Vertical angles are made by two intersecting lines.
Unless I am misunderstanding something due to any possible formatting issues in the question's text, this statement as been proved with one statement. Was it intended to be ΔLMQ ≅ ΔPMN? If so, let me know and I will edit my answer. I interpreted ALMQ~ APMN to mean angle LMQ and angle PMN, if this is not the case, in the future, you can copy and paste the Δ symbol online or say "triangle" instead of "A".
