Chapter 4.2, Problem 41PPS

To determine

The inequality to describe the possible measure of angle Z.

Answer to Problem 41PPS

The inequality to describe the possible value of z is $0<z<23.$

Explanation of Solution

Given:

  $m\angle X=157,m\angle Y=y,m\angle Z=z.$

Calculation:

The sum of all the angles of a triangle is 180.

Therefore,

  $\begin{array}{l}m\angle X+m\angle Y+m\angle Z=180\\ 157+y+z=180\\ y+z=23\end{array}$

As the measure of an angle is positive. Therefore, y is greater than 0, hence;

  $\begin{array}{l}z=23-y\\ z<23\end{array}$

The inequality to describe the possible value of z is $0<z<23.$