The sum of the interior angles of a triangle is one of the differences between Euclidean and spherical geometries. Which of the following interior angle measures of a triangle belong to spherical geometry?

A.30°, 60°, 90°

B.35°, 60°, 80°

C.20°, 60°, 100°

D.65°, 60°, 60°

In **Euclidean geometry**, the sum of the interior angles of a triangle is always **180°**. However, in **spherical geometry**, the sum of the interior angles of a triangle is always **greater than 180°**. This occurs because triangles are drawn on the surface of a sphere, where the curvature of the surface affects the angles.

Now, let's analyze the given options:

- **A. 30°, 60°, 90°** → Sum = 180° (belongs to Euclidean geometry, not spherical)
- **B. 35°, 60°, 80°** → Sum = 175° (belongs to neither Euclidean nor spherical geometry)
- **C. 20°, 60°, 100°** → Sum = 180° (belongs to Euclidean geometry, not spherical)
- **D. 65°, 60°, 60°** → Sum = 185° (greater than 180°, belongs to spherical geometry)

Thus, **D. 65°, 60°, 60°** belongs to **spherical geometry**.

Would you like further clarification on this concept or on spherical geometry in general?

Here are five related questions:
1. How is the sum of the interior angles of a triangle calculated in spherical geometry?
2. What real-world applications use spherical geometry?
3. How does curvature affect the properties of triangles in spherical geometry?
4. Can a triangle in spherical geometry have angles less than 180°?
5. What is the significance of "geodesics" in spherical geometry?

**Tip**: In spherical geometry, the larger the area of the triangle on the sphere, the larger the sum of its angles!

The sum of the interior angles of a triangle is one of the differences between Euclidean and spherical geometries. Which of the following interior angle measures of a triangle belong to spherical geometry? A.30°, 60°, 90° B.35°, 60°, 80° C.20°, 60°, 100° D.65°, 60°, 60°

Explore the differences between Euclidean and spherical geometry with a focus on the sum of the interior angles of triangles. This problem compares angle sums, explaining why D. 65°, 60°, 60° belongs to spherical geometry. Ideal for Grades 9-12 students.

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