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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.
You could say the measure of angle A is equal to the measure of angle B. But in geometry, the correct way to say it is angles A and B are congruent. To be congruent the only requirement is that the angle measure be the same, the length of the two arms making up the angle is irrelevant.