(b) let ( mathbf{v}=langle 1,-2\rangle ) and ( mathbf{w}=langle-2,3\rangle ). what is the angle formed…

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles add up to (180^{\circ}). So, ((3x + 1)+(2x + 4)=180).

Step2: Solve the equation for (x)

Combine like terms: (3x+2x+1 + 4=180), which simplifies to (5x+5 = 180). Subtract (5) from both sides: (5x=180 - 5=175). Divide both sides by (5): (x=\frac{175}{5}=35).

Step3: Find the measures of the angles

For the first angle: (3x + 1=3\times35+1=105 + 1=106^{\circ}). For the second angle: (2x + 4=2\times35+4=70+4=74^{\circ}).

Answer:

A. (106^{\circ}) and (74^{\circ})