1. **State the problem:** We have a circle with center O and two radii forming an angle of 42° at the center. We need to find the value of the angle $x$ at the circumference subtended by the same arc. 2. **Recall the circle theorem:** The angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference. 3. **Apply the theorem:** If the central angle is $42^\circ$, then the angle at the circumference $x$ is given by: $$x = \frac{42^\circ}{2}$$ 4. **Calculate:** $$x = 21^\circ$$ 5. **Conclusion:** The value of $x$ is $21^\circ$.