\( U \) If \( O Q \) and \( R T \) are parallel lines and \( \angle Q P S=77^{\circ} \), what is \( \angle N P O \) ? A \( 73^{\circ} \) B \( 77^{\circ} \) C \( 93^{\circ} \) D \( 103^{\circ} \)

To solve for \( \angle N P O \), we can use the properties of parallel lines and the angles formed by a transversal. 1. **Identify the angles**: Since \( O Q \) and \( R T \) are parallel lines, and \( P S \) is a transversal, we can use the corresponding angles theorem. This theorem states that if a transversal intersects two parallel lines, then each pair of corresponding angles is equal. 2. **Given information**: We know that \( \angle Q P S = 77^{\circ} \). 3. **Determine the corresponding angle**: The angle \( \angle N P O \) is a corresponding angle to \( \angle Q P S \) because they are both formed by the transversal \( P S \) intersecting the parallel lines \( O Q \) and \( R T \). 4. **Conclusion**: Since corresponding angles are equal, we have: \[ \angle N P O = \angle Q P S = 77^{\circ} \] Thus, the answer is \( \angle N P O = 77^{\circ} \). The correct option is **B \( 77^{\circ} \)**.