1. **State the problem:** We need to find the value of the unknown angle $x^\circ$ in a figure where angles 43°, 42°, and 120° are given along a horizontal line. 2. **Understand the geometry:** The angles around a point on a straight line sum up to 180° because a straight line forms a straight angle. 3. **Set up the equation:** The sum of the angles on the straight line is $$43^\circ + 42^\circ + 120^\circ + x^\circ = 180^\circ$$ 4. **Calculate the sum of the known angles:** $$43 + 42 + 120 = 205$$ 5. **Write the equation with the sum:** $$205 + x = 180$$ 6. **Solve for $x$:** $$x = 180 - 205$$ $$x = -25$$ 7. **Interpretation:** Since an angle cannot be negative in this context, this suggests the angles given do not lie on the same straight line or there is an error in the problem setup. However, if the problem intends the angles to be around a point (360° total), then we can check that: Sum of given angles plus $x$ equals 360°: $$43 + 42 + 120 + x = 360$$ $$205 + x = 360$$ $$x = 360 - 205$$ $$x = 155$$ Thus, the value of $x$ is $155^\circ$ assuming the angles are around a point. **Final answer:** $$x = 155^\circ$$