Question

1. find the value of x.

x =

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. The sum of \((7x - 1)^{\circ}\) and \((6x - 1)^{\circ}\) is \(180^{\circ}\) (they form a linear - pair). So, we have the equation \((7x - 1)+(6x - 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+6x-1 - 1=180\), which simplifies to \(13x-2 = 180\).

Step3: Solve for \(x\)

Add \(2\) to both sides of the equation: \(13x-2 + 2=180 + 2\), so \(13x=182\). Then divide both sides by \(13\): \(x=\frac{182}{13}\).

Answer:

\(x = 14\)