1. **State the problem:** We have a right-angled triangle with hypotenuse length 14 cm, an adjacent side to angle $x$ of length 7 cm, and angle $x$ to find. 2. **Identify the trigonometric ratio needed:** Since we know the hypotenuse and adjacent side, use cosine which relates adjacent and hypotenuse: $$\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{7}{14} = \frac{1}{2}$$ 3. **Solve for $x$:** Find the angle whose cosine is $\frac{1}{2}$: $$x = \cos^{-1}\left(\frac{1}{2}\right)$$ From standard angles, $\cos 60^\circ = \frac{1}{2}$. 4. **Final answer:** $$x = 60^\circ$$ The exact value of $x$ is $60$ degrees.