Question

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what is the value of x?
enter your answer in the box.

Explanation:

Step1: Set up the equation

Since the two angles are vertical angles, they are equal. So \(4x + 7=5(x - 4)\)

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(4x + 7 = 5x-20\)

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(4x-4x + 7=5x-4x-20\), which simplifies to \(7=x - 20\)
Then add \(20\) to both sides: \(x=7 + 20\)

Answer:

\(x = 9\)