Question

1. set up an equation and solve for $x$: $x =$ $(x^{2}+6x + 2)^{circ}$ $(x^{2}+2x + 10)^{circ}$

Explanation:

Step1: Set up the equation

Since the two angles are vertical angles, they are equal. So we set up the equation \(x^{2}+6x + 2=x^{2}+2x+10\).

Step2: Simplify the equation

Subtract \(x^{2}\) from both sides of the equation:
\(x^{2}-x^{2}+6x + 2=x^{2}-x^{2}+2x+10\)
\(6x + 2=2x+10\)

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(6x-2x + 2=2x-2x+10\), which gives \(4x+2 = 10\).
Then subtract \(2\) from both sides: \(4x+2-2=10 - 2\), so \(4x=8\).
Divide both sides by \(4\): \(x=\frac{8}{4}\).

Answer:

\(x = 2\)