Question

m∠2=(2y - 7)° and m∠4=(y + 17)°. what is m∠2?

Explanation:

Step1: Identify angle relationship

$\angle2$ and $\angle4$ are vertical - angles, so $m\angle2 = m\angle4$.

Step2: Set up the equation

$2y - 7=y + 17$.

Step3: Solve for y

Subtract y from both sides: $2y-y-7=y - y+17$, which gives $y - 7=17$. Then add 7 to both sides: $y-7 + 7=17 + 7$, so $y = 24$.

Step4: Find $m\angle2$

Substitute $y = 24$ into the expression for $m\angle2$: $m\angle2=2y-7=2\times24 - 7=48 - 7=41$.

Answer:

41