1. **State the problem:** We have a triangle with angles 51°, 86°, and two unknown angles labeled $x$ inside the triangle. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always 180°. This means: $$51^\circ + 86^\circ + x + x = 180^\circ$$ 3. **Set up the equation:** Combine like terms: $$51 + 86 + 2x = 180$$ 4. **Simplify the constants:** $$137 + 2x = 180$$ 5. **Isolate $x$:** Subtract 137 from both sides: $$\cancel{137} + 2x - \cancel{137} = 180 - 137$$ $$2x = 43$$ 6. **Solve for $x$:** Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{43}{\cancel{2}}$$ $$x = 21.5^\circ$$ **Final answer:** Each angle labeled $x$ measures $21.5^\circ$.