1. **State the problem:** We have a right triangle IHG with a right angle at H. Given: IH = 9.5, GH = 4.1, and we need to find angle $x$ at vertex G. 2. **Identify the sides relative to angle $x$:** - Side opposite angle $x$ is IH = 9.5 - Side adjacent to angle $x$ is GH = 4.1 3. **Formula used:** To find an angle in a right triangle, use the tangent function: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** $$\tan(x) = \frac{9.5}{4.1}$$ 5. **Calculate the ratio:** $$\tan(x) = 2.3170731707$$ 6. **Find angle $x$ by taking the arctangent:** $$x = \tan^{-1}(2.3170731707)$$ 7. **Calculate $x$ using a calculator:** $$x \approx 66.1^\circ$$ **Final answer:** $$x \approx 66.1^\circ$$