Question

question
∠1 and ∠2 are vertical angles. if m∠1=(3x + 22)° and m∠2=(7x - 22)°, then find the value of x.
answer attempt 1 out of 8

Explanation:

Step1: Set up the equation

Since vertical - angles are equal, we set \(m\angle1=m\angle2\). So, \(3x + 22=7x-22\).

Step2: Move x - terms to one side

Subtract \(3x\) from both sides: \(3x+22 - 3x=7x - 22-3x\), which simplifies to \(22 = 4x-22\).

Step3: Move constant to the other side

Add 22 to both sides: \(22 + 22=4x-22 + 22\), getting \(44 = 4x\).

Step4: Solve for x

Divide both sides by 4: \(\frac{44}{4}=\frac{4x}{4}\), so \(x = 11\).

Answer:

\(x = 11\)