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Interior of an Angle
From Latin: interior - "inner"
Definition: The area between the rays that make up an angle, and extending away from the vertex to infinity.
Try this Drag an orange dot. The point K will indicate if it is within the interior of angle ABC (shown in yellow). Or, drag the point K.

The interior of an angle is the area between the two rays that define it, shown in yellow above. Even if the angle is made up of line segments and so have a finite length, the interior extends beyond them forever. In the figure above, drag the point K and notice that it is in the interior of ABC even beyond the ends of the line segments BA and BC forming the angle.

NOTE: Do not confuse this with the interior angles of triangles and other polygons.
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Other angle topics

General

Angle Types

Angle relationships