Question

1. ∠x and ∠y are vertical angles.
2. ____________
3. given
4. vertical angle theorem

Explanation:

Step1: Recall the Vertical Angle Theorem

The Vertical Angle Theorem states that vertical angles are congruent.

Step2: Apply the theorem to the given angles

Since \(∠X\) and \(∠Y\) are vertical angles (given), by the Vertical Angle Theorem, \(∠X\cong∠Y\).

Answer:

\(∠X\cong∠Y\)