Question

∠1 and ∠2 are vertical angles. the m∠1 = 8x + 1 and m∠2 = 4x + 25. what is the measure of angle 2?

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1=m\angle2$.

Step2: Set up the equation

Set $8x + 1=4x+25$.

Step3: Solve for $x$

Subtract $4x$ from both sides: $8x - 4x+1=4x - 4x + 25$, which simplifies to $4x+1 = 25$. Then subtract 1 from both sides: $4x+1 - 1=25 - 1$, getting $4x=24$. Divide both sides by 4: $x = 6$.

Step4: Find the measure of $\angle2$

Substitute $x = 6$ into the expression for $m\angle2$. $m\angle2=4x + 25=4\times6+25=24 + 25=49$.

Answer:

$49$