There are 360 degrees in a convex quadrilateral. A convex quadrilateral is made up of four sides and four corners, or angles. None of the angles bend inward toward the center of the shape, and the degrees of all four angles always add up to 360 degrees.
A convex quadrilateral can be divided into two triangles by drawing a line from the vertex of one angle to the vertex of the nonadjacent angle in the quadrilateral. The fact that there are 180 degrees in a triangle creates the basis of a geometric proof regarding the number of degrees in the quadrilateral.
Quadrilaterals with angles that bend inwards are called nonconvex quadrilaterals. Totaling the degrees for all four angles in a nonconvex quadrilateral may result in more than 360 degrees.