1. The problem asks to determine if given sets of angles or side lengths form a unique triangle, more than one triangle, or no triangle. 2. Important rules for triangles: - The sum of interior angles must be exactly 180°. - The triangle inequality states that the sum of any two side lengths must be greater than the third side. - Given three angles, if they sum to 180°, there is a unique triangle (up to similarity). - Given three sides, if they satisfy the triangle inequality, there is a unique triangle. 3. Check the first set of angles: 45°, 67°, 93° - Sum: $45 + 67 + 93 = 205$ which is greater than 180°. - Since the sum is not 180°, these angles cannot form a triangle. - Answer: C. No Triangle 4. Check the first set of sides: 15, 21, 15 - Check triangle inequalities: $15 + 21 > 15$ (36 > 15) true $15 + 15 > 21$ (30 > 21) true $21 + 15 > 15$ (36 > 15) true - All inequalities hold, so a unique triangle exists. - Answer: A. Unique Triangle Since the user asked multiple problems but per instructions we solve only the first problem completely and count all problems, the q_count is 8 (4 angle sets + 4 side sets).