Question

∠1 and ∠2 are vertical angles. if m∠1=(8x - 10)° and m∠2=(5x + 2)°, then find the value of x.

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we have $8x - 10=5x + 2$.

Step2: Move x - terms to one side

Subtract $5x$ from both sides: $8x-5x - 10=5x-5x + 2$, which simplifies to $3x-10 = 2$.

Step3: Isolate the variable term

Add 10 to both sides: $3x-10 + 10=2 + 10$, resulting in $3x=12$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{12}{3}$, so $x = 4$.

Answer:

$4$