Geometry

Question Analysis

This question involves the concept of vertical angles in geometry.

Key Concept Explanation

Vertical angles are formed when two lines intersect. They are non - adjacent angles such that the sides of one angle are the opposite rays of the sides of the other angle. Vertical angles are always congruent.

Step-by-Step Solution

1. Examine each pair of angles. First, determine the two lines that intersect to form each angle in the pair.

2. Check if the angles are non - adjacent and formed by the same two intersecting lines. If both conditions are met, they are vertical angles.

Option Analysis

A.∠XTS & ∠XTZ: Both ∠XTS and ∠XTZ are formed by the intersection of lines SZ and XR. However, they are adjacent angles as they share a common side (ray XT), so this pair is not vertical angles.

B.∠XTS & ∠ZTR: ∠XTS and ∠ZTR are both formed by the intersection of lines SZ and XR, and they are non - adjacent. Thus, this pair is vertical angles.

C.∠ZTR & ∠STR: ∠ZTR and ∠STR are formed by the intersection of lines SZ and XR, but they are adjacent angles (shar...