Question

1. name two adjacent angles. 13. name two vertical angles. 14. find m∠suv. refer to the figure. example 3 lesson 2 - 1 · angles and congruence 71

Explanation:

Step1: Recall adjacent - angles definition

Adjacent angles share a common side and a common vertex. In the figure, $\angle USW$ and $\angle WSM$ share side $\overrightarrow{SW}$ and vertex $S$. Also, $\angle QSR$ and $\angle RSP$ share side $\overrightarrow{SR}$ and vertex $R$.

Step2: Recall vertical - angles definition

Vertical angles are formed when two lines intersect. In the figure, if we consider the intersection of lines (formed by the rays), $\angle QSN$ and $\angle RSP$ are vertical angles. Also, $\angle QSR$ and $\angle NSP$ are vertical angles.

Step3: Find $\angle SUV$

$\angle SUV$ and the $58^{\circ}$ angle are complementary (since the angle formed at $S$ with a right - angle symbol). Complementary angles add up to $90^{\circ}$. Let $m\angle SUV=x$. Then $x + 58^{\circ}=90^{\circ}$. Solving for $x$ gives $x=90^{\circ}-58^{\circ}=32^{\circ}$.

Answer:

1. $\angle USW$ and $\angle WSM$, $\angle QSR$ and $\angle RSP$
2. $\angle QSN$ and $\angle RSP$, $\angle QSR$ and $\angle NSP$
3. $32^{\circ}$