Question

a
$(65x - 12)^{circ}$
$(43x + 10)^{circ}$

Explanation:

Step1: Set up the equation

Vertical angles are equal. So, \(65x - 12=43x + 10\).

Step2: Solve for \(x\)

Subtract \(43x\) from both sides: \(65x-43x - 12=43x-43x + 10\), which simplifies to \(22x-12 = 10\).
Add \(12\) to both sides: \(22x-12 + 12=10 + 12\), getting \(22x=22\).
Divide both sides by \(22\): \(x=\frac{22}{22}=1\).

Answer:

\(x = 1\)