1. **Stating the problem:** We have two parallel lines PQ and RS cut by a transversal XY. We need to identify corresponding angles and find the values of angles \(\angle a\) and \(\angle b\) in the given diagrams. 2. **Corresponding angles rule:** When a transversal cuts two parallel lines, corresponding angles are equal. 3. **Answering the blanks:** - a) \(\angle a\) and \(\angle e\) are corresponding angles. - b) \(\angle d\) and \(\angle h\) are corresponding angles. - c) \(\angle b\) and \(\angle f\) are corresponding angles. - d) \(\angle c\) and \(\angle g\) are corresponding angles. 4. **Finding \(\angle a\) and \(\angle b\):** - Given angles at the top intersections are 85° and 95°. - Since the lines are parallel, \(\angle a\) and \(\angle b\) are interior angles on the same side of the transversal. - Interior angles on the same side of a transversal sum to 180°. 5. **Calculations:** - \(\angle a = 180° - 85° = 95°\) - \(\angle b = 180° - 95° = 85°\) 6. **Reasons:** - \(\angle a\) and 85° are interior angles on the same side of the transversal, so they sum to 180°. - \(\angle b\) and 95° are interior angles on the same side of the transversal, so they sum to 180°. **Final answers:** - \(\angle a = 95°\) - \(\angle b = 85°\)