$\begin{align}  & F\overset{\wedge }{\mathop{B}}\,D=A\overset{\wedge }{\mathop{B}}\,P={{30}^{\circ }}\text{  (vertically opposite angles)} \\ & \text{consider }\Delta BDF \\ & F\overset{\wedge }{\mathop{B}}\,D+B\overset{\wedge }{\mathop{D}}\,F+B\overset{\wedge }{\mathop{F}}\,D=\text{ (sum of }\angle \text{s in a }\Delta \text{)} \\ & {{50}^{\circ }}+{{30}^{\circ }}+B\overset{\wedge }{\mathop{F}}\,D={{180}^{\circ }} \\ & B\overset{\wedge }{\mathop{F}}\,D= \\ & B\overset{\wedge }{\mathop{F}}\,D+Q\overset{\wedge }{\mathop{F}}\,D=\text{ (sum of }\angle \text{s on a straight line)} \\ & {{100}^{\circ }}+Q\overset{\wedge }{\mathop{F}}\,D={{180}^{\circ }} \\ & x=Q\overset{\wedge }{\mathop{F}}\,D={{80}^{\circ }} \\\end{align}$