$\begin{align}  & \angle BD{{G}_{reflex}}+\angle BD{{G}_{acute}}={{360}^{\circ }}\text{    }\!\!\{\!\!\text{ Angle at a point }\!\!\}\!\!\text{ } \\ & \text{26}{{\text{0}}^{\circ }}+\angle BD{{G}_{acute}}={{360}^{\circ }} \\ & \angle BD{{G}_{acute}}={{100}^{\circ }} \\ & \angle GDE=\angle FGD\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & \angle BD{{G}_{acute}}=\angle GDE+\angle BDE \\ & {{100}^{\circ }}={{30}^{\circ }}+\angle BDE \\ & \angle BDE={{70}^{\circ }} \\ & x=\angle ABD=\angle BDE={{70}^{\circ }}\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{  } \\\end{align}$