Question

∠1 and ∠2 are vertical angles. if (mangle1=(7x - 23)^{circ}) and (mangle2=(6x + 4)^{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, $7x - 23=6x + 4$.

Step2: Isolate the variable x

Subtract $6x$ from both sides: $7x-6x - 23=6x-6x + 4$, which simplifies to $x-23 = 4$.

Step3: Solve for x

Add 23 to both sides: $x-23 + 23=4 + 23$. So, $x=27$.

Answer:

$x = 27$