Please explain (said question) surrounding a proof of 2 equal angles

I would firstly ask them how much they knew about trigonometry, and then guide them through the SoHCaHToA theory. I would use diagrams for this. I would then ask them to spot any ways they could work out any additional angles in the shape, using other theories such as Pythagoras, or basic ideas about the degrees in certain shapes. If they were still confused, I would hint and guide them through the most appropriate use of sin, cos or tan in order to calculate any remaining angles that could be worked out. While I would use the maths problem that they presented, I would also ensure that they have full sound knowledge of the other trigonometric theories and possibly present them with some additional problems that we could work on together in the tutoring session.