The question asks:

"Which of the following cannot be the sum of the measures of the angles in a triangle in spherical geometry? Select all that apply."

Key Concept:

In spherical geometry, the sum of the angles in a triangle is always greater than 180° but less than 540°. This is because the curvature of the sphere causes the angles to be larger than in Euclidean geometry (where the sum is exactly 180°).

Let's analyze each option:

• A. 270° – This is possible since it is greater than 180° and less than 540°.
• B. 140° – This is not possible, as the sum must be greater than 180° in spherical geometry.
• C. 195° – This is possible, as it is greater than 180° and less than 540°.
• D. 180° – This is not possible, as it equals 180°, which occurs only in Euclidean geometry.
• E. 265° – This is possible, as it is greater than 180° and less than 540°.

Therefore, the correct answers are:

• B. 140°
• D. 180°

Would you like more details or further clarification?

Here are 5 related questions to explore the concept:

1. What is the sum of the angles in a triangle in Euclidean geometry?
2. How does spherical geometry differ from Euclidean geometry?
3. Can a triangle in spherical geometry have an angle sum of 360°?
4. What is the relationship between the area of a spherical triangle and its angle sum?
5. How does the curvature of a sphere affect the properties of triangles?

Tip: In spherical geometry, always check if the angle sum is greater than 180° when determining if a value is valid.