A spherical triangle is a shape created on a sphere's surface by three great circle arcs meeting at each of its three vertices pairwise. A few important facts regarding spherical triangles are:
-The sides are not lines; rather, they are the arcs of huge circles. -Every side is quantified by its arc length, which is commonly represented as an angle at the sphere's centre. -A spherical triangle's total angles are always larger than 180° and less than 540°. -Any two sides added together always equal more than the third side.
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The "angle" meant in your third item is the angle measured on the surface of the sphere (and "> 180°" means the surface has positive curvature/isn't flat), but you can certainly have a spherical triangle where each side subtends only a fraction of a degree (the "angle" you first mention), so that the sum of the angles describing the sides is well under 180°, or even 1°.
