Question

1. in the diagram shown, $overline{qw}$ and $overline{sv}$ intersect at point $r$ and $overline{rt}$ is drawn such that $angle srt=angle wrt$. (a) name a linear pair of angles from the diagram. (b) name a pair of vertical angles from the diagram. (c) if $mangle srt = 70^{circ}$, then find the measure of $angle qrv$ and the measure of $angle qrs$.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Since $\angle SRT$ and $\angle QRV$ are vertical angles, $m\angle QRV=m\angle SRT$.

Step2: Determine $m\angle QRV$

Given $m\angle SRT = 70^{\circ}$, so $m\angle QRV=70^{\circ}$.

Step3: Recall linear - pair property

$\angle SRT$ and $\angle S RQ$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle SRT+m\angle S RQ = 180^{\circ}$.

Step4: Determine $m\angle S RQ$

$m\angle S RQ=180^{\circ}-m\angle SRT$. Substituting $m\angle SRT = 70^{\circ}$, we get $m\angle S RQ = 180 - 70=110^{\circ}$. And $\angle S RQ$ and $\angle QRS$ are the same angle, so $m\angle QRS = 110^{\circ}$.

Answer:

$m\angle QRV = 70^{\circ}$, $m\angle QRS=110^{\circ}$