1. **State the problem:** We need to solve for $x$ given two angles: one is $(2x + 41)^\circ$ and the other is $51^\circ$. 2. **Understand the relationship:** The two angles are on a straight line at point $R$, so they are supplementary angles. Supplementary angles add up to $180^\circ$. 3. **Write the equation:** $$ (2x + 41) + 51 = 180 $$ 4. **Simplify the equation:** $$ 2x + 41 + 51 = 180 $$ $$ 2x + 92 = 180 $$ 5. **Isolate $x$:** $$ 2x = 180 - 92 $$ $$ 2x = 88 $$ 6. **Divide both sides by 2:** $$ x = \frac{88}{2} $$ $$ x = \cancel{\frac{88}{2}} 44 $$ 7. **Final answer:** $$ x = 44 $$