Question

find the value of b.

Explanation:

Step1: Use angle - sum property

The two angles $(b + 70)^{\circ}$ and $(-b + 74)^{\circ}$ are supplementary, so their sum is $180^{\circ}$. We set up the equation $(b + 70)+(-b + 74)=180$.

Step2: Simplify the left - hand side

Combining like terms, $b - b+70 + 74=180$, which simplifies to $144 = 180$. This is incorrect. The correct relationship is that they are vertical angles (assuming the lines are intersecting), and vertical angles are equal. So we set up the equation $b + 70=-b + 74$.

Step3: Solve for $b$

Add $b$ to both sides: $b + b+70=-b + b+74$, which gives $2b+70 = 74$. Then subtract 70 from both sides: $2b+70 - 70=74 - 70$, so $2b = 4$. Divide both sides by 2: $\frac{2b}{2}=\frac{4}{2}$, and $b = 2$.

Answer:

$2$