Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume the two angles $(3x + 62)^{\circ}$ and $(89-6x)^{\circ}$ are vertical angles (since no other information about the relationship is given and vertical angles are equal when two lines intersect). Set up the equation $3x + 62=89 - 6x$.

Step2: Isolate the variable terms

Add $6x$ to both sides of the equation: $3x+6x + 62=89-6x+6x$, which simplifies to $9x + 62=89$.

Step3: Isolate the variable

Subtract 62 from both sides: $9x+62 - 62=89 - 62$, resulting in $9x=27$.

Step4: Solve for x

Divide both sides by 9: $\frac{9x}{9}=\frac{27}{9}$, so $x = 3$.

Answer:

$3$