How are the interior and exterior angles of a triangle related?

How are the interior and exterior angles of a triangle related?

Answers (1)

By the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles (the angles that do not form a linear pair with the exterior angle).
Consider \(\displaystyle\triangle{A}{B}{C}\) below:
The exterior angle measures \(\displaystyle{m}\angle{A}{C}{D}={110}∘\) and the two remote interior angles have a sum of \(\displaystyle{m}\angle{A}+{m}\angle{B}={60}∘+{50}∘={110}∘\). Therefore \(\displaystyle{m}\angle{A}{C}{D}={m}\angle{A}+{m}\angle{B}\).

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