Why does the triangle drawn on Earth have angle sum greater than 180°?

Conditions

• The triangle is drawn on the surface of a sphere (Earth).
• The geometry is spherical geometry.

Reasoning, step by step

1. Observe the angle labels on the spherical triangle (e.g., 90°, 90°, and 50°).
2. Add the angles to find the sum (230°).
3. Compare the sum to 180° to confirm it is greater.
4. Relate this to the rule that spherical triangles have an angle sum >180° due to positive curvature.

Example

The video shows a large white triangle on a rotating Earth model with visible angle labels 90°, 90°, and 50°, summing to 230°, which is greater than 180°.

Common misconceptions

• Assuming that the angle sum is 180° because it looks like a standard triangle on a flat map.
• Believing that the angle sum depends on the size of the triangle rather than the curvature of the surface.

Watch the explanation

Explore next

• If a sphere is not Euclidean, why can small triangles on Earth be nearly 180°?
• What is the difference between global spherical geometry and local Euclidean approximation in this clip?