Definition
Interior
The interior of a closed shape is the region inside its boundary.
What it means
Picture the boundary as a fence. Points enclosed by the fence are in the interior. Points exactly on the fence are boundary points, and points beyond it are in the exterior.
Remember it
Interior means enclosed inside the edge, not on the edge.
Example
For a circle, the centre is an interior point. A point exactly on the circumference is a boundary point, while a point farther away than the radius is in the exterior.
Watch for
The everyday phrase inside a shape may casually include its edge. The strict interior excludes all boundary points.
Common mix-up
An interior angle is a particular angle inside a polygon; it is not the entire interior region.
Exact meaning
For a closed plane figure or region, the interior is the set of points inside its boundary. In the strict geometric sense, boundary points are not part of the interior.