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 $angle qrs$. 7. in a linear angle pair, the measure of the larger angle is 15 degrees less than twice the measure of the smaller

Explanation:

Step1: Recall linear - pair property

A linear - pair of angles are adjacent and supplementary. From the diagram, $\angle SRQ$ and $\angle SRT$ form a linear pair.

Step2: Recall vertical - angles property

Vertical angles are opposite angles formed by the intersection of two lines. $\angle SRQ$ and $\angle WRV$ are vertical angles.

Step3: Find $\angle QRV$

Since $\angle SRT=\angle WRT = 70^{\circ}$ and $\angle QRV$ and $\angle SRT$ are vertical angles, $\angle QRV=\angle SRT = 70^{\circ}$.

Step4: Find $\angle QRS$

$\angle QRS$ and $\angle SRT$ form a linear - pair. So, $\angle QRS=180^{\circ}-\angle SRT$. Substituting $\angle SRT = 70^{\circ}$, we get $\angle QRS = 180 - 70=110^{\circ}$.

Answer:

(a) $\angle SRQ$ and $\angle SRT$
(b) $\angle SRQ$ and $\angle WRV$
(c) $m\angle QRV = 70^{\circ}$, $m\angle QRS=110^{\circ}$