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There are many runway intersections that are not 90 degree turns. They are frequently mid runway so typically only used by smaller planes for departure

Cleared to takeoff can be given before you have entered the runway, or you can be asked to “lineup and wait”.

The first means that you have permission to enter the runway, if you haven’t already, and takeoff. The latter means that you are cleared to enter the runway, but not takeoff and wait for takeoff clearance.