Question

question
∠1 and ∠2 are vertical angles. if m∠1=(4x - 7)° and m∠2=(x + 17)°, then find the value of x.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle1 = m\angle2$. So, $4x - 7=x + 17$.

Step2: Isolate the variable terms

Subtract $x$ from both sides: $4x - x-7=x - x + 17$, which simplifies to $3x-7 = 17$.

Step3: Isolate the variable

Add 7 to both sides: $3x-7 + 7=17 + 7$, getting $3x=24$.

Step4: Solve for $x$

Divide both sides by 3: $\frac{3x}{3}=\frac{24}{3}$, so $x = 8$.

Answer:

$8$