Solving Long Answer Problems Involving Multiple Triangles

The CST exam always features a question where triangles are seemingly “stuck” to other triangles, and an unknown value (angle or side) is stuck in the middle of a multi-triangle figure. How do you solve one of these questions fully and completely? Sine law, metric relations, Pythagorean theorem, and SOH CAH TOA (if your teacher uses it) can all be helpful or necessary.