Question

∠1 and ∠2 are vertical angles. if (mangle1=(4x - 7)^{circ}) and (mangle2=(x + 17)^{circ}), 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 further

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:

$x = 8$