Chapter 4.2, Problem 51HP

To determine

To explain:

Reason for triangle cannot have an obtuse, acute and right exterior angle.

Answer to Problem 51HP

Reason for triangle cannot have an obtuse, acute and right exterior angle is contradiction to angle sum theorem.

Explanation of Solution

Exterior angles are supplementary (add to $180°$ ) to their respective interior angles.

This relationship limits the exterior angles too.

No triangle can have interior angles that are both right $\left(90°\right)$ and obtuse $\left(>90°\right)$ .

This would contradict the angle sum theorem, without even adding the third angle, the sum would be greater than $180°$ .