1. **Problem statement:** Given a quadrilateral ABCD, decompose it into triangles by drawing segments from vertex A to all non-adjacent vertices. 2. **Decomposition:** The non-adjacent vertices to A are C only (since B and D are adjacent). Drawing segment AC divides the quadrilateral into two triangles: \(\triangle ABC\) and \(\triangle ACD\). 3. **Number of triangles formed:** There are 2 triangles formed by this decomposition. 4. **Sum of angle measures in one triangle:** The sum of interior angles in any triangle is always \(180^\circ\). 5. **Sum of angle measures in the quadrilateral:** Since the quadrilateral is decomposed into 2 triangles, the sum of its interior angles is \(2 \times 180^\circ = 360^\circ\). 6. **General formula for sum of interior angles in an n-sided convex polygon:** The sum is given by \((n - 2) \times 180^\circ\). This formula comes from decomposing the polygon into \(n-2\) triangles, each with interior angles summing to \(180^\circ\).