To determine which set of angle measures cannot form a triangle, we use the basic rule that the sum of the interior angles of any triangle is always 180°.

Let's check each option:

Option A: 65°, 65°, 50°

• 65° + 65° + 50° = 180°
  This is valid because the sum is 180°.

Option B: 54.3°, 47.5°, 78.2°

• 54.3° + 47.5° + 78.2° = 180°
  This is valid because the sum is 180°.

Option C: 22.5°, 36.4°, 110.1°

• 22.5° + 36.4° + 110.1° = 169°
  This is not valid because the sum is less than 180°, which means these angles cannot form a triangle.

Option D: 40°, 40°, 100°

• 40° + 40° + 100° = 180°
  This is valid because the sum is 180°.

Conclusion:

The set of angle measures C. 22.5°, 36.4°, 110.1° cannot form a triangle because the sum of the angles is less than 180°.

Would you like a detailed explanation of why this rule applies to all triangles, or have any other questions? Here are some related questions to explore:

1. What is the relationship between the interior and exterior angles of a triangle?
2. Can an equilateral triangle have angles that are not equal to 60°?
3. How can we calculate the missing angle of a triangle when two angles are known?
4. What is the sum of the interior angles of a polygon with n sides?
5. What is the difference between acute, obtuse, and right triangles?

Tip: Always remember that the sum of angles in any triangle must be 180°!