1. **Problem statement:** We are given a quadrilateral WUTV with diagonals WT and UV, where WT is parallel to UV. We need to find: a) The size of angle TUV. b) The size of angle VWT. 2. **Given information:** - Angle WTU (at T) = 106° - Angle WVU (at V) = 68° - WT \parallel UV 3. **Key rules and formulas:** - When two lines are parallel, alternate interior angles are equal. - The sum of angles in a triangle is 180°. 4. **Find angle TUV (angle at U between T and V):** - Consider triangle TUV. - We know WT \parallel UV, so angle WTU = angle TUV (alternate interior angles). - Therefore, angle TUV = 106°. 5. **Find angle VWT (angle at W between V and T):** - Consider triangle WUV. - Angle WVU = 68° (given). - Since WT \parallel UV, angle WTU = angle TUV = 106° (from step 4). - In triangle WUT, sum of angles = 180°: $$\angle VWT + 106^\circ + 68^\circ = 180^\circ$$ - Simplify: $$\angle VWT + 174^\circ = 180^\circ$$ - Subtract 174° from both sides: $$\angle VWT = 180^\circ - 174^\circ = 6^\circ$$ **Final answers:** - a) $\angle TUV = 106^\circ$ - b) $\angle VWT = 6^\circ$