An interior angle that is a multiple of the exterior angle

Each interior angle of a regular \(n\)-sided polygon is \(k\) times each of its exterior angles, where \(k\) is a positive whole number.

1. Find \(n\) when \(k=4\).[1]
2. Show that \(n=2k+2\) for every value of \(k\), and explain why \(n\) is always even.[3]
3. A regular polygon has interior angle \(165^\circ\). Find \(n\) and \(k\).[1]
4. The exterior angle of a regular \(n\)-sided polygon is \(15^\circ\) larger than the exterior angle of a regular \(2n\)-sided polygon. Find \(n\).[2]