Question

if m∠2 = 9x - 12 and m∠4 = 6x + 30, what is m∠6 and m∠8?

Explanation:

Step1: Identify angle - relationship

$\angle2$ and $\angle4$ are vertical angles, so $m\angle2 = m\angle4$.
$9x - 12=6x + 30$

Step2: Solve for $x$

Subtract $6x$ from both sides: $9x-6x - 12=6x-6x + 30$, which gives $3x-12 = 30$.
Add 12 to both sides: $3x-12 + 12=30 + 12$, so $3x=42$.
Divide both sides by 3: $x = 14$.

Step3: Find $m\angle2$

Substitute $x = 14$ into the expression for $m\angle2$: $m\angle2=9x - 12=9\times14-12=126 - 12=114^{\circ}$.

Step4: Find $m\angle6$

$\angle2$ and $\angle6$ are corresponding angles, so $m\angle6=m\angle2 = 114^{\circ}$.

Step5: Find $m\angle8$

$\angle4$ and $\angle8$ are corresponding angles. First, find $m\angle4$: $m\angle4=6x + 30=6\times14+30=84 + 30=114^{\circ}$, so $m\angle8=m\angle4 = 114^{\circ}$.

Answer:

$m\angle6 = 114^{\circ}$, $m\angle8 = 114^{\circ}$