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You say the "inside" and not the interior angles, so you could mean the inside temperature which would exceed 180 degrees if the triangle was in, for example, a pot of boiling water. Is this what you meant or did you actually mean the interior angles? If you meant the interior angles, then from my geometry classes, they always add to 180 degrees for any triangle.

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You say the "inside" and not the interior angles, so you could mean the inside temperature which would exceed 180 degrees if the triangle was in, for example, a pot of boiling water. Is this what you meant or did you actually mean the interior angles? If you meant the interior angles, then from my geometry classes, they always add to 180 degrees for any triangle.

Best answer so far haha.

But yeah as far as I know it is impossible to have the interior angles equal anything but 180 degrees. However it states sum of the interior... anything?

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Wolfram MathWorld

Spherical Triangle

A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the spherical analog of the planar triangle, and is sometimes called an Euler triangle (Harris and Stocker 1998). ...

The sum of the angles of a spherical triangle is between Pi and 3Pi radians (180 and 540 degrees; Zwillinger 1995, p. 469). The amount by which it exceeds 180 degrees is called the spherical excess ...

On any sphere, if three connecting arcs are drawn, two triangles are created. If each triangle takes up one hemisphere, then they are equal in size, but in general there will be one larger and one smaller. Any spherical triangle can therefore be considered both an inner and outer triangle, with the inner triangle usually being assumed. The sum of the angles of an outer spherical triangle is between 3Pi and 5Pi radians.

The study of angles and distances of figures on a sphere is known as spherical trigonometry.

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referring to temperature, as multiple people have mentioned -or- maybe the triangle has other lines inside it forming other angles. If you add upp all the angles formed by the lines inside the triangle you get mroe than 180.

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What is the largest possible sum of angles?

Follow-on question:

Can the sum of angles of a triangle be less than 180o?

How small can that sum be?

Spherical triangles are pi < sum <= 3pi radians (cant remember if it's <= or strictly <). Which is 180 through 540 degrees.

Trinagles projected on a hyperbolic plane the sum of the angles as 0 <= sum < pi radians, which is 0 through 180. I know there are triangles on the hyperbolic plane that can sum the angles to zero.

In fact, i believe that you can tell the geometry system (hyperbolic, euclidean, spherical) in which you are working if you know the sum of the angles, since they are mutually exclusive of each other

Edited by tpaxatb
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What is the largest possible sum of angles?

Follow-on question:

Can the sum of angles of a triangle be less than 180o?

How small can that sum be?

0 degrees, when the (curved) lines each connecting two corners are tangent to each other in every corner:

post-19783-12476864110057.jpg

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