Question

The hexagon GIKMPR and triangle FJN are regular. the dashed line segments form 30 degrees angles.

Answer 1

Comment
When you go through 180 degrees, what happens is that you follow a straight line until you hit something on the other side of the line.

For example 

A ___________∨____________B

If you start at A and go through ∨ and onward to B, you have effectively gone through a rotation of 180o. 

Just to nail it down, in a rotation through 90° you would travel through a right angle like this one. ⊥ You would start on one of the horizontal ends and when you hit the vertical line you would go up 90° from where you started. If you go clockwise, N would be where R is for 90°.

Answer
You don't want 90 you want 180. I've just done that to explain it a little better.

NO would become OH <<<<<< answer. 

Answer 2

Solution:

As ON is a line segment , and ∠ ON P = 90°= ∠ON M

There are two cases

1. When line segment ON is rotated in clockwise direction by an angle 180°.

  When ON rotated by an angle of 90° in clockwise Direction it reaches OR and then again by 90° take it to OH.

2.  When line segment ON is rotated in anticlockwise direction by an angle 180°.

  When ON rotated by an angle of 90° in Anticlockwise Direction it reaches OK and then again by 90° take it to OH.

So in both the cases segment ON becomes OH i.e N →H.