$\begin{align}  & \mathbf{Construction}:\text{Draw a line}DF\text{ parallel to }GI\text{ and }AC\text{ to pass through point }E \\ & \angle BEH={{360}^{o}}-{{260}^{o}}\text{    }\!\!\{\!\!\text{ sum of angles at a point }\!\!\}\!\!\text{ } \\ & \angle BEH={{100}^{o}} \\ & \angle BEF=\angle ABE\text{ =5}{{\text{5}}^{o}}\text{   }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & \angle HEF=\angle GHE={{x}^{o}}\text{    }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & \angle BEH={{55}^{o}}+{{x}^{o}} \\ & 100=55+{{x}^{o}} \\ & {{x}^{o}}={{100}^{o}}-{{55}^{o}}={{45}^{o}} \\\end{align}$