# Sum of interior angles of a quadrilateral

## INTERIOR AND EXTERIOR OF A QUADRILATERAL

Consider a quadrilateral ABCD. Clearly, it is a plane figure. All points in the plane of quadrilateral ABCD are divided into following three parts:

 (i) The part of the plane made up by all such points as are enclosed by quadrilateral ABCD. This part of the plane is called the interior of the quadrilateral ABCD and any point of this part is called an interior point of the quadrilateral. In figure P is an interior point of quadrilateral ABCD. (ii) The part of the plane made up by all-points as are not enclosed by the quadrilateral ABCD. This part of the plane is called the exterior of the quadrilateral ABCD and any point of this part is called an exterior point of the quadrilateral. Clearly, quadrilateral ABCD is the boundary of its interior and it separates interior of quadrilateral from its exterior.

 The quadrilateral EFGH shown in figure (ii) is not a convex quadrilateral, because the vertices E and F lie on the opposite side of line GH.  In a convex quadrilateral the line segment joining any two points in its interior lies completely in its interior. In a convex quadrilateral the measure of each angle is less than 180º. Both the diagonals of a convex quadrilateral lie wholly in its interior.