Carol Gates
2021-01-23
Answered

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

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Nola Robson

Answered 2021-01-24
Author has **94** answers

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$\mathrm{\u25b3}ABC$ below:

The exterior angle measures$m\mathrm{\angle}ACD=110\circ$ and the two remote interior angles have a sum of $m\mathrm{\angle}A+m\mathrm{\angle}B=60\circ +50\circ =110\circ$ . Therefore $m\mathrm{\angle}ACD=m\mathrm{\angle}A+m\mathrm{\angle}B$ .

Consider

The exterior angle measures

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