Our friend is incorrect. Explanation: See solution.
Practice makes perfect
According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Let's explain why.
The Triangle Sum Theorem states that in any given triangle, the measure of the interior angles add up to 180^(∘).
Next, let's draw an exterior angle to one of the three angles in our triangle.
The orange exterior angle along with the blue angle, form a linear pair. By the Linear Pair Postulate they are supplementary angles and therefore add up to 180^(∘)
By the Congruent Supplements Theorem, we can say that the orange angle is congruent to the sum of the red and green angles. This means that the measure of the nonadjacent angles is always going to be equal to the exterior angle which is exactly what the Exterior Angle Theorem says. We thus conclude that our friend is incorrect.
