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 are formed by the same two intersecting lines. If both conditions are met, they are vertical angles.

Option Analysis

A.∠XTW & ∠YTR: Both ∠XTW and ∠YTR are formed by the intersection of lines XR and WY. Also, they are non - adjacent. So, this pair is vertical angles.

B.∠XTW & ∠ZTY: ∠XTW is formed by lines XR and WY, while ∠ZTY is formed by lines SZ and WY. Since they are not formed by the same two lines, this pair is not vertical angles.

C.∠YTR & ∠STW: ∠YTR is formed by lines XR and WY, and ∠STW is formed by lines SZ and WY. As they are formed by different pairs of lines, this pair ...