1. **Problem Statement:** Determine which sets of measurements could be the interior angle measures of a triangle and which sets could be the side lengths of a triangle. 2. **Triangle Angle Sum Rule:** The sum of the interior angles of a triangle is always $$180^\circ$$. 3. **Check each angle set:** - (a) A: $$10^\circ + 10^\circ + 160^\circ = 180^\circ$$ ✓ Possible - (a) B: $$15^\circ + 75^\circ + 90^\circ = 180^\circ$$ ✓ Possible - (a) C: $$20^\circ + 80^\circ + 100^\circ = 200^\circ$$ ✗ Not possible - (a) D: $$35^\circ + 35^\circ + 105^\circ = 175^\circ$$ ✗ Not possible - (a) E: $$60^\circ + 60^\circ + 60^\circ = 180^\circ$$ ✓ Possible 4. **Triangle Side Length Rule (Triangle Inequality):** For any triangle with sides $$a$$, $$b$$, and $$c$$, the sum of any two sides must be greater than the third side: $$a + b > c$$ $$a + c > b$$ $$b + c > a$$ 5. **Check each side length set:** - (b) A: $$3 + 3 > 3$$ (6 > 3) ✓, $$3 + 3 > 3$$ (6 > 3) ✓, $$3 + 3 > 3$$ (6 > 3) ✓ Possible - (b) B: $$4 + 8 > 13$$ (12 > 13) ✗ Not possible **Final answers:** - (a) Possible angle sets: A, B, E - (b) Possible side length set: A