Question

if m∠2 = 9x - 12 and m∠4 = 6x + 30, what is m∠2 and m∠1?

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: $x=\frac{42}{3}=14$.

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 $m\angle1$

$\angle1$ and $\angle2$ are a linear - pair, so $m\angle1+m\angle2 = 180^{\circ}$.
$m\angle1=180 - m\angle2=180 - 114 = 66^{\circ}$.

Answer:

$m\angle2 = 114^{\circ}$, $m\angle1 = 66^{\circ}$