Video narration
Why do the inside angles of every four-sided shape add to the same total, even when the shape looks different? Imagine your quadrilateral, a four-sided shape, drawn on a sheet of paper. Its corners can be wide, narrow, or uneven. Draw one diagonal from a corner to the opposite corner. This line is a proof tool, not an extra side. Now notice: the diagonal splits the quadrilateral into two triangles. The corner angles are shared between them. Each triangle has angles totaling 180 degrees, so together they give 180 plus 180, or 360 degrees. So appearance does not matter. A square and an irregular quadrilateral have the same total. As long as the shape is simple and closed, its four inside angles add to 360 degrees. So why the same total? On your sheet, one diagonal makes two triangles: 180 degrees plus 180 degrees equals 360 degrees.