To determine which set of angle measures would not be possible in a triangle, we need to recall the triangle angle sum property: the sum of the angles in any triangle must always be 180°.

Now, let's check each option:

A. 25°, 50°, 105°

• Sum: $25° + 50° + 105° = 180°$
• Possible: This is a valid triangle because the sum is 180°.

B. 40°, 65°, 75°

• Sum: $40° + 65° + 75° = 180°$
• Possible: This is a valid triangle because the sum is 180°.

C. 45°, 45°, 90°

• Sum: $45° + 45° + 90° = 180°$
• Possible: This is a valid triangle, specifically a right triangle (since it has a 90° angle).

D. 50°, 65°, 80°

• Sum: $50° + 65° + 80° = 195°$
• Not Possible: The sum exceeds 180°, so this cannot form a triangle.

Answer: D. 50°, 65°, 80° is not possible because the sum of the angles is greater than 180°.

Would you like further explanation on any of the steps? Or do you have any other questions?

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Here are some related questions to explore:

1. What happens if the sum of angles in a triangle is less than 180°?
2. How do the angles of an equilateral triangle compare to the angle sum property?
3. What is the difference between acute, obtuse, and right triangles in terms of their angles?
4. Can a triangle have more than one 90° angle?
5. How can the angles in a non-Euclidean triangle differ from those in Euclidean geometry?

Tip: Always remember that the sum of the angles in a triangle is 180°—if you encounter a set where the sum is different, it cannot be a triangle!