Chapter 2.8, Problem 31HP

To determine

To draw: The angle $WXZ$ such that $m\angle WXZ=45$ .then prove your conjecture.

Answer to Problem 31HP

The angle $m\angle WXZ=45$ is shown in figure (1) and the right angle is proof $m\angle WXY=90$ .

Explanation of Solution

Given information:

The given function is a conjecture as to the measure of $\angle WXY$ .

Calculation:

Draw the figure as given in the question.

  

Figure (1)

Place compass point at $X$ , draw an arc that intersect both rays of $\angle WXZ$ .

Place compass point at $W$ , and open the compass to the distance between $WandZ$ .

Label the point $Y$ where the two arc intersect.

Draw $\overrightarrow{XY}$ as shown in the figure (2).

  

Figure (2)

  $\begin{array}{c}m\angle XYZ=m\angle WXZ\\ m\angle YXZ+M\angle WXZ=M\angle WXY\\ m\angle WXZ+M\angle WXZ=M\angle WXY\\ 2m\angle WXZ=m\angle WXY\end{array}$

  $\begin{array}{c}2\times 45=m\angle WXY\\ m\angle WXY=90\end{array}$

Therefore, the angle $m\angle WXZ=45$ is shown in figure (1) and the right angle is proof $m\angle WXY=90$ .