1. The problem: Explain the triangle angle sum rule. 2. The triangle angle sum rule states that the sum of the interior angles of any triangle is always equal to 180 degrees. 3. Formula: $$\angle A + \angle B + \angle C = 180^\circ$$ where $\angle A$, $\angle B$, and $\angle C$ are the three interior angles of the triangle. 4. Important rule: This applies to all triangles, whether they are scalene, isosceles, or equilateral. 5. Explanation: If you know two angles of a triangle, you can find the third by subtracting the sum of the known angles from 180 degrees. 6. Example: Suppose $\angle A = 50^\circ$ and $\angle B = 60^\circ$. Then, $$\angle C = 180^\circ - (50^\circ + 60^\circ) = 180^\circ - 110^\circ = 70^\circ$$ 7. This rule helps in solving many geometry problems involving triangles by allowing you to find missing angles easily.