Question

∠1 and ∠2 are vertical angles. if m∠1=(6x + 16)° and m∠2=(8x + 20)°, then find the value of x.

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set \(m\angle1 = m\angle2\), so \(6x + 16=8x + 20\).

Step2: Move x - terms to one side

Subtract \(6x\) from both sides: \(16 = 8x-6x + 20\), which simplifies to \(16 = 2x+20\).

Step3: Move constant to one side

Subtract 20 from both sides: \(16 - 20=2x\), so \(- 4 = 2x\).

Step4: Solve for x

Divide both sides by 2: \(x=\frac{-4}{2}=-2\).

Answer:

\(-2\)