\[\begin{align}  & \cos (x+{{40}^{\circ }})=0.0872 \\ & x+{{40}^{\circ }}={{\cos }^{-1}}(0.0872) \\ & x+{{40}^{\circ }}={{84.9974}^{\circ }} \\ & x+{{40}^{\circ }}\simeq {{85}^{\circ }} \\ & x={{45}^{\circ }} \\\end{align}\]