Final answer:
The value of w in the figure to the nearest degree is 45° (option D).
Step-by-step explanation:
The value of w in the figure to the nearest degree is 45° (option D).
In the given equation, T₁ sin (30°) + T₂ sin (45°) = w, we can substitute the expression for T₂ in terms of T₁ to reduce the equation to one unknown.
Therefore, the value of w in the figure is 45°.