Question

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

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are formed when two lines intersect. They are non - adjacent angles opposite each other.

Step2: Analyze each pair

• For $\angle WSI$ and $\angle ISK$, they are adjacent, so not vertical angles.
• For $\angle KSW$ and $\angle NST$, they are vertical angles as they are non - adjacent and formed by the intersection of lines $KW$ and $NT$ at point $S$.
• For $\angle TSN$ and $\angle ISW$, they are vertical angles as they are non - adjacent and formed by the intersection of lines $KW$ and $NT$ at point $S$.
• For $\angle ISN$ and $\angle TSW$, they are adjacent, so not vertical angles.

Answer:

$\angle KSW$ and $\angle NST$, $\angle TSN$ and $\angle ISW$