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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.
But we also know the angles in the triangle add to 180 o: , so . Since and are both equal to , they are equal to each other by the transitive property: . Here is an obvious result that follows immediately: Corollary to the Exterior Angle Theorem. The measure of an exterior angle is always greater than the measure of either remote interior angle. Proof: In the above setup, . If we drop one of the measures on the right, we have or since angles always have positive measure. Relation between Angles and Sides of a Triangle