How many sides does the triangle add up to?

Answer 1

The three interior angles of a plane triangle add up to 180 degrees, or pi radians.

If the sum is not 180° you are not in Euclidean space.

If the three angles of a triangle add up to more than 180° then you are in a spherical space, if the sum is less than 180° it is a hyperbolic space.

Example:Think of a triangle on the Earth with one corner at the North Pole, the other corners on the Equator 90° apart (say at 0° [west of Nigeria in Africa] the other at 90° W [West of Ecuador in South America]).

Each of these angles is 90° so the sum is 270° -

The surface area of the triangle is one eighth of the surface of the globe. But it is a triangle (on a sphere)!

On a plane, always 180 degrees. If the sum is not 180° you are not in Euclidean (flat) space.

If the three angles of a triangle add up to more than 180° then you are in a spherical space, if the sum is less than 180° it is a hyperbolic space.

Example:

Think of a triangle on the Earth with one corner at the North Pole, the other corners on the Equator 90° apart (say at 0° [west of Nigeria in Africa] the other at 90° W [West of Ecuador in South America]).

Each of these angles is 90° so the sum is 270° -

The surface area of the triangle is one eighth of the surface of the globe. But it is a triangle (on a sphere)!

The sum of the internal angles of any triangle is 180 degrees.

Answer 2

Triangles always have 3 sides. The interior angles add up to 180 degrees.

Answer 3

The sum of the interior angles of an obtuse triangle as with all triangles is 180 degrees.

Answer 4

180 degrees

Answer 5

180