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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.
The sum of two acute angles is either acute, right or obtuse. The sum of an obtuse and an acute angle, or of three acute angles, may be reflex. The existence (or admittance) of reflex angles kills all hope that the interior of an angle may be determined from its sides in a natural way.