Question

find the value of x.

Explanation:

Step1: Identify angle - relationship

Assume the two angles are supplementary (since no other angle - relationship is indicated and they seem to be on the same side of the transversal). The sum of two supplementary angles is 180°. So, $(7x + 12)+(3x - 2)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $7x+3x+12 - 2=180$, which simplifies to $10x + 10=180$.

Step3: Isolate the variable term

Subtract 10 from both sides: $10x=180 - 10$, so $10x=170$.

Step4: Solve for x

Divide both sides by 10: $x=\frac{170}{10}=17$.

Answer:

$x = 17$