Chapter 4.2, Problem 50HP

To determine

To explain:

Reason for given triangle is obtuse or acute or right when exterior angle adjacent to $\angle A$ is acute.

Answer to Problem 50HP

The triangle $△ABC$ is obtuse, as it has an obtuse angle.

Explanation of Solution

Given information:

Condition: If exterior angle adjacent to $\angle A$ is acute.

If the exterior angle is acute, then the adjacent angle is obtuse

As these two angles form a linear pair.

  

  $m\angle DAC+m\angle CAB=180°$

The angles $DAC$ and $CAB$ form a angles thus, we have:

  $m\angle CAB$ Belongs to $△ABC$ , that means $△ABC$ is obtuse.