1. The problem states that two angles are supplementary, meaning their measures add up to 180 degrees. 2. Given: - $m \angle 1 = 50^\circ$ - $m \angle 2 = (4x + 10)^\circ$ 3. The formula for supplementary angles is: $$m \angle 1 + m \angle 2 = 180$$ 4. Substitute the given values: $$50 + (4x + 10) = 180$$ 5. Simplify the equation: $$50 + 4x + 10 = 180$$ $$4x + 60 = 180$$ 6. Subtract 60 from both sides: $$4x + \cancel{60} - \cancel{60} = 180 - 60$$ $$4x = 120$$ 7. Divide both sides by 4: $$\frac{4x}{\cancel{4}} = \frac{120}{\cancel{4}}$$ $$x = 30$$ 8. Therefore, the value of $x$ is 30. Final answer: $x = 30$ (Option A)