Question

if the measure of ∠4 is (8x + 4)° and the measure of ∠6 is (6x + 28)°, what is the value of x?

Explanation:

Step1: Identify angle relationship

$\angle4$ and $\angle6$ are alternate - interior angles. For parallel lines, alternate - interior angles are equal. So, $8x + 4=6x + 28$.

Step2: Solve the equation for x

Subtract $6x$ from both sides: $8x-6x + 4=6x-6x + 28$, which simplifies to $2x+4 = 28$.

Step3: Isolate the variable term

Subtract 4 from both sides: $2x+4 - 4=28 - 4$, getting $2x=24$.

Step4: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{24}{2}$, so $x = 12$.

Answer:

$x = 12$