Segments uv and wz are parallel with line st intersecting both at points q and r respectively

according to the given information, segment uv is parallel to segment wz while angles squ and vqt are vertical angles. angle vqt is congruent to angle squ by the vertical angles theorem. because angles squ and wrs are angles, they are congruent according to the angles postulate. finally, angle vqt is congruent to angle wrs.