Question

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Explanation:

Step1: Find the measure of ∠1

Since ∠1 and the \(120^{\circ}\) angle are vertical angles, they are equal.
\(\angle1 = 120^{\circ}\)

Step2: Find the measure of ∠2

Because the two horizontal lines are parallel, ∠1 and ∠2 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.
\(\angle2=\angle1\)
Substitute \(\angle1 = 120^{\circ}\) into the equation.
\(\angle2 = 120^{\circ}\)

Answer:

\(\angle1 = 120^{\circ}\), \(\angle2 = 120^{\circ}\)