Question

m∠2 = 6x - 28
m∠8 = 3x + 50
what is the measure of ∠2?

Explanation:

Step1: Identify angle - relationship

$\angle2$ and $\angle8$ are corresponding angles, so $m\angle2 = m\angle8$. Then we set up the equation $6x - 28=3x + 50$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $6x-3x - 28=3x-3x + 50$, which simplifies to $3x-28 = 50$. Then add 28 to both sides: $3x-28 + 28=50 + 28$, getting $3x=78$. Divide both sides by 3: $x=\frac{78}{3}=26$.

Step3: Find $m\angle2$

Substitute $x = 26$ into the expression for $m\angle2$. So $m\angle2=6x - 28=6\times26-28=156 - 28 = 128$.

Answer:

$128$