Chapter 4, Problem 3CUR

To determine

To complete: the blank in the given statement.

Answer to Problem 3CUR

Obtuse angle

Explanation of Solution

Given information:

The given statement is “ $\overrightarrow{BD}$ bisects $\angle ABC,m\angle ABC=5x-4,$ and

$m\angle CBD=2x+10,\angle ABC$ is $a\left(n\right)$

  $\underset{\_}{}$ angle”..

By using property of bisector

  $m\angle ABC=2m\angle CBD$

  $\begin{array}{l}5x-4=2(2x+10)\\ 5x-4=2(2x)+2(10)\\ 5x-4=4x+20\\ 5x-4x=20+4\\ \Rightarrow x=24\end{array}$

Then,

  $m\angle ABC=5(24)-4=116$

Since the measure of the angle is greater than 90 degrees but less than 180 degrees, $\angle ABC$ is an obtuse angle.

Hence, the blank is filled with term obtuse angle.