1. **State the problem:** We are given that ABC is a straight line parallel to DF, with BD = DE. We know angle p = 64° from the given data. We need to find the angles q, r, and s. 2. **Find q:** Since BD = DE, triangle BDE is isosceles with BD = DE. Angles opposite equal sides are equal, so angles at B and E in triangle BDE are equal. Angle at B next to p is 80°, so angle at E (which is q) is also 80°. 3. **Find r:** Since ABC and DF are parallel and BC and EF act as transversals, angles corresponding to angle at C (36°) on line DEF match angle r. Thus, angle r = 36° (corresponding angles between parallel lines). 4. **Find s:** Angles on straight line DEF add to 180°. We know angles q = 80° and r = 36°, so: $$ s = 180° - (q + r) = 180° - (80° + 36°) = 180° - 116° = 64° $$ **Final answers:** (a) $p = 64°$ (b) $q = 80°$ (c) $r = 36°$ (d) $s = 64°$