Chapter 13, Problem 1CUR

To determine

To identify: $\angle ABC$ is acute, obtuse, or right.

Answer to Problem 1CUR

The $\angle ABC$ is obtuse.

Explanation of Solution

Given information: $\overrightarrow{BD}$ bisects $\angle ABC$ , $m\angle ABC=5x-4$ and $m\angle CBD=\frac{3}{2}x+21$ .

Calculation:

  $\begin{array}{l}\theta =\frac{3x}{2}+21\\ 2\theta =5x-4\\ \frac{1}{2}=\frac{\frac{3x}{2}+21}{5x-4}\\ 5x-4=3x+42\\ 2x=46\\ x=23\\ \angle ABC=2\theta \\ \Rightarrow 5x-4\\ \Rightarrow 5\left(23\right)-4\\ \Rightarrow 115-4\\ \Rightarrow 111\end{array}$

So, $\angle ABC$ is obtuse.