Question

1. ( mangle abc )

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary.
$$x + 116=180$$

Step2: Solve for \(x\)

Subtract \(116\) from both sides of the equation.
$$x=180 - 116$$
$$x = 64$$

Step3: Use the property of vertical angles

\(\angle ABC\) and \(x\) are vertical angles. Vertical angles are equal.
So \(m\angle ABC=x\)

Answer:

\(64^{\circ}\)