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prove that in any triangle,each external angles is equal to the sum of the internal angles at the other 2 vertices
Referring to the Figure, the Theorem states that the exterior angle BCD is equal to the sum of angles BAC and ABC.

The proof is very simple. First, for the sum of angles BCD and BCA we have
    BCD + BCA = 180°,
as these angles are supplementary .
From the other side, the sum of the interior angles of the triangle ABC is equal to 180°:
    BAC + ABC + BCA = 180°,
as we proved it before. Comparing these two equalities, you can conclude that
    BAC + ABC = BCD,
 The proof is completed.


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