Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume that the angles $(56 - 5x)^{\circ}$ and $(62 - 8x)^{\circ}$ are vertical angles. Vertical angles are equal. So we set up the equation $56-5x = 62 - 8x$.

Step2: Solve the equation for x

Add $8x$ to both sides of the equation: $56-5x + 8x=62 - 8x+8x$, which simplifies to $56 + 3x=62$.

Step3: Isolate the variable term

Subtract 56 from both sides: $56 + 3x-56=62 - 56$, resulting in $3x = 6$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{6}{3}$, so $x = 2$.

Answer:

$2$