1. The problem is to determine which angle is congruent to \(\angle HUI\) from the given options: \(\angle GUI\), \(\angle IGU\), or \(\angle UIG\). 2. Congruent angles have the same measure. To find the congruent angle, we need to understand the order of letters in angle notation: the middle letter represents the vertex of the angle. 3. \(\angle HUI\) has vertex \(U\), so the congruent angle must also have vertex \(U\). 4. Among the options, \(\angle UIG\) has vertex \(U\), matching the vertex of \(\angle HUI\). 5. Therefore, \(\angle HUI \cong \angle UIG\). Final answer: \(\boxed{\angle UIG}\) is congruent to \(\angle HUI\).