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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.
We also know that since the dotted line is parallel to BC that by alternate interior angles. This gives us: Substituting for angles 1 and 2 we have This result is true for all triangles: Summarizing:Theorem: The sum of the three angles in a triangle is always 180Âº. Let's Practice:If two of the three angles in a triangle have measure 34Âº and 72Âº, what is the measure of the third angle? We have 34Âº + 72Âº = 106Âº. Therefore the third angle has a measure of 180Âº - 106Âº = 74Âº In a triangle ABC, we have.