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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.
Theorem 1.7.4: Any two right angles are congruent. Given :  ABC is a right angle. DEF is a right angle. Prove: ABC # DEF Theorem 1.7.5: If the exterior sides of two adjacent angles form perpendicular rays, then theses angles are complementary. Theorem 2.1.1: From a point not on a given line, there is exactly one line perpendicular to the given point.