Question

x - 28 = x + 2

Explanation:

Step1: Set up equation for first - pair of angles

Assume the two angles $(3x - 28)^{\circ}$ and $(x + 2)^{\circ}$ are either vertical angles or corresponding angles (if the lines are parallel). So we set up the equation $3x-28=x + 2$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $3x-x-28=x - x+2$, which simplifies to $2x-28 = 2$. Then add 28 to both sides: $2x-28 + 28=2 + 28$, getting $2x=30$. Divide both sides by 2: $x=\frac{30}{2}=15$.

Step3: Check with second - pair of angles (if needed)

For the second - pair of angles $(2x + 12)^{\circ}$ and $6x^{\circ}$, if they are supplementary (sum to $180^{\circ}$), we check. First, substitute $x = 15$ into the angles. The first angle is $2x+12=2\times15 + 12=30 + 12=42^{\circ}$, and the second angle is $6x=6\times15 = 90^{\circ}$. Since $42^{\circ}+90^{\circ}
eq180^{\circ}$, we focus on the first equation result.

Answer:

$x = 15$