Question

Why do the poles experience about six monyhs day and six momths night

Answer 1

Due to the curvature of the earth the rays do not reach the polar region properly.so they experience 6 month day and 6 months night

Answer 2

It isn't full daylight or full darkness as we experience at latitudes away from the polar circles.  During the 6 months of "day", the Sun circles around just above  the horizon.

During the 6 months of night, it circles just below the horizon, so it isn't full darkness.

The Earth's axis is tipped about 23.5 degrees with respect to the plane of the ecliptic. 

So that's why it is 6 months dark 6 months day in Antarctica and the Arctic region :)