Since a circle has 360 degrees, a compass has 360 degrees, too.
North is at 0 degrees.
The cardinal points divide the circle into 4 equal parts.
360 divided by 4 = 90, so the cardinal points are 90 degrees apart.
Therefore:
North=0East=90South=180West=270

The intercardinal points mark the midway point between the cardinal points.
90 divided by 2 = 45
Therefore:
NE = 45SE = 135SW = 225NW = 315

Note that the cardinal points are also 90 degrees apart, because there are four of them.

The secondary intercardinal points mark the midway points between the cardinal points and intercardinal points.

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