In the diagram $\angle QPR={{60}^{\circ }},\text{ }\angle PQR={{50}^{\circ }},\text{ }QRS=2{{x}^{\circ }},\text{ }\angle SRP=3{{x}^{\circ }},\text{ }\angle UQP={{y}^{\circ }}$ and $RS\parallel TU$calculate y
102o
78o
70o
60o
$\begin{align} & \text{In }\vartriangle PQR \\ & {{50}^{\circ }}+{{60}^{\circ }}+(2x+3x)={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle s\text{ in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & x={{14}^{\circ }} \\ & 2x=2\times {{14}^{\circ }}={{28}^{\circ }} \\ & \angle TQR=\angle SRQ={{28}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & \text{Consider the line }UT\text{ at point }Q \\ & y+{{50}^{\circ }}+{{28}^{\circ }}={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ Sum of angles on a straight line }\!\!\}\!\!\text{ } \\ & y={{102}^{\circ }} \\\end{align}$