Question

which pairs of angles in the figure below are vertical angles? check all that apply. a. ∠isn and ∠tsw b. ∠tsn and ∠isw c. ∠wsi and ∠isk d. ∠ksw and ∠nst

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures.

Step2: Analyze Option A

$\angle ISN$ and $\angle TSW$ are formed by the intersection of lines $NT$ and $KW$ at point $S$. They are opposite each other, so they are vertical angles.

Step3: Analyze Option B

$\angle TSN$ and $\angle ISW$ are also formed by the intersection of lines $NT$ and $KW$ at point $S$. They are opposite each other, so they are vertical angles.

Step4: Analyze Option C

$\angle WSI$ and $\angle ISK$ share a common side ($\overrightarrow{SI}$) and are adjacent - angles, not vertical angles.

Step5: Analyze Option D

$\angle KSW$ and $\angle NST$ are formed by the intersection of lines $NT$ and $KW$ at point $S$. They are opposite each other, so they are vertical angles.

Answer:

A. $\angle ISN$ and $\angle TSW$
B. $\angle TSN$ and $\angle ISW$
D. $\angle KSW$ and $\angle NST$