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In Euclidean geometry, the sum of the angles Î± + Î² + Î³ is equal to two right angles (180Â° or Ï radians). This allows determination of the third angle of any triangle as soon as two angles are known. should IMHO be: In Euclidean geometry, the sum of the internal angles is a straight angle. This allows determining the amplitude of the third internal angle of any triangle once the amplitudes of the others are known. Similar confusions exist between segments and their lengths.
In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180Â°, Ï radians, two right angles, or a half-turn. It was unknown for a long time whether other geometries exist, where this sum is different.