Question

1. find the value of x. 5) find the value of x.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. In the second problem, the angles \((5x + 1)^{\circ}\) and \((6x+3)^{\circ}\) are vertical angles. So we set up the equation \(5x + 1=6x + 3\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides of the equation: \(5x+1-5x=6x + 3-5x\). This simplifies to \(1=x + 3\). Then subtract 3 from both sides: \(1-3=x+3 - 3\), which gives \(x=-2\).

Answer:

\(x=-2\)