1. **State the problem:** Determine which combinations of angle types can form the angles of a triangle. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $$180^\circ$$. 3. **Important angle type definitions:** - Acute angle: less than $$90^\circ$$ - Right angle: exactly $$90^\circ$$ - Obtuse angle: greater than $$90^\circ$$ but less than $$180^\circ$$ 4. **Analyze each combination:** - A: Acute, acute, right - Two acute angles (each < $$90^\circ$$) plus one right angle ($$90^\circ$$) sum to $$180^\circ$$. - Possible because $$<90 + <90 + 90 = 180$$. - B: Obtuse, acute, obtuse - Two obtuse angles (each > $$90^\circ$$) plus one acute angle. - Sum would be greater than $$90 + 90 + 0 = 180$$, which is impossible. - Not possible. - C: Acute, acute, acute - Three acute angles each less than $$90^\circ$$. - Sum can be exactly $$180^\circ$$ (e.g., $$60^\circ + 60^\circ + 60^\circ$$). - Possible. - D: Acute, acute, obtuse - Two acute angles plus one obtuse angle. - Sum can be exactly $$180^\circ$$ (e.g., $$40^\circ + 50^\circ + 90^\circ$$). - Possible. - E: Right, acute, right - Two right angles ($$90^\circ$$ each) plus one acute angle. - Sum would be $$90 + 90 + <90 = >180$$, which is impossible. - Not possible. **Final answer:** The possible combinations are A, C, and D.