Question

∠a and ∠b are vertical angles with m∠a = x and m∠b = 3x - 60. what is m∠a? enter your answer in the box.

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So \(m\angle A=m\angle B\).
Since \(m\angle A = x\) and \(m\angle B=3x - 60\), we have the equation \(x=3x - 60\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(0 = 3x-x - 60\), which simplifies to \(0 = 2x-60\).
Add \(60\) to both sides: \(2x=60\).
Divide both sides by \(2\): \(x = 30\).
Since \(m\angle A=x\), then \(m\angle A = 30\).

Answer:

\(30\)