Chapter 14.4, Problem 35WE

To determine

To show: One angle between $l\&l\text{'}$ has measure $x$ .

Answer to Problem 35WE

Angles between $l\&l\text{'}$ lines one of the angle measure is $x^{°}$ .

Explanation of Solution

Given information :

A rotation $R_O$ maps line $l\&l\text{'}$ .

Concept used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

As per the given problem,

  $\overline{OF}$ perpendicular from $O$ to $l$ rotating through $x^{°}$ , its image will be $\overline{OF\text{'}}$ .

  

  $\begin{array}{l}\overline{OF}\perp l\\ \overline{OF\text{'}}\perp l\text{'}\end{array}$

  

  $ENFO$ is a quadrilateral.

  $\angle EOF+\angle OFN+\angle FNE+\angle NEO={360}^{°}$

  $\begin{array}{l}\angle OFN={90}^{°}\\ \angle NEO={90}^{°}\end{array}$

As per question, $\angle EOF=x^{°}$

Thus,

  $\angle ENF={(180-x)}^{°}$

  $\angle ENF+\angle lNl\text{'}={180}^{°}$ (Adjacent angles)

  $\angle lNl\text{'}=x^{°}$ (angles between lines $l\&l\text{'}$ )

Hence,

Angles between $l\&l\text{'}$ lines one of the angle measure is $x^{°}$ .