1. The problem asks to solve using simple angle chasing with a solution style suitable for an IMO gold medal level in geometry. 2. Start by identifying all given angles and considering the properties of triangles, cyclic quadrilaterals, or parallel lines if applicable. 3. Apply the angle sum property in triangles: $$\text{sum of angles in a triangle} = 180^\circ$$. 4. Use the exterior angle theorem when needed: $$\text{exterior angle} = \text{sum of opposite interior angles}$$. 5. Identify any isosceles or equilateral triangles which allow angle equivalences. 6. If a cyclic quadrilateral is involved, recall that opposite angles sum to $$180^\circ$$. 7. Combine these properties stepwise to express unknown angles in terms of known ones and solve. 8. Conclude the solution by calculating the required angle(s) fully simplified. This methodological approach ensures a concise, elegant IMO gold style solution using simple angle chasing techniques.