Question

the diagram below shows the function $r_{b,75}(sv)$. use the diagram to answer the remaining questions. line segment sv was rotated through a ° angle of rotation. the measure of line segment sv is equal to the measure of line segment. the measure of ∠sbs and the measure of ∠vbv are both equal to. the measure of $vv$ and the measure of $ss$ are both equal to °.

Explanation:

Step1: Identify angle of rotation

The notation $R_{B,75}(\overline{SV})$ indicates a rotation of line - segment $\overline{SV}$ about point $B$ by an angle of $75^{\circ}$. So the angle of rotation is $75^{\circ}$.

Step2: Recall property of rotation

A rotation is a rigid transformation. Rigid transformations preserve the lengths of line - segments. So, if $\overline{SV}$ is rotated to $\overline{S'V'}$, then $S'V'=SV$.

Step3: Recall angle of rotation property

The angle of rotation is equal to the measure of the angle formed by a point, its image, and the center of rotation. So, $\angle SBS'=\angle VBV' = 75^{\circ}$.

Step4: Recall arc - measure property

The measure of an arc is equal to the measure of the central angle that intercepts it. Since the angle of rotation is $75^{\circ}$, the measure of arc $\widehat{VV'}$ and arc $\widehat{SS'}$ is $75^{\circ}$.

Answer:

1. $75$
2. $SV$
3. $75^{\circ}$
4. $75$