Concept:Use corresponding angles, angles on a straight line, and the total interior angle sum of a quadrilateral.Explanation:Extend QR to meet TU at V.Since PQ∥TU, the corresponding angle relation gives:∠RVT=∠PQR=50∘.At R, QRV is a straight line, so:∠VRS=180∘−86∘=94∘.At T, UTV is a straight line, so:∠VTS=180∘−64∘=116∘.The angles of quadrilateral RVTS sum to 360∘.Therefore:50∘+94∘+116∘+x=360∘x+260∘=360∘x=100∘.
