Question

question 1 1 pts
if ( mangle1 ) is ( 120^{circ} ), what is the measure of ( mangle3 )?

Explanation:

Step1: Identify the relationship between ∠1 and ∠2

∠1 and ∠2 are supplementary angles (they form a linear pair).
$$m\angle1 + m\angle2=180^{\circ}$$
Given \(m\angle1 = 120^{\circ}\), then \(120^{\circ}+m\angle2 = 180^{\circ}\), so \(m\angle2=180^{\circ}- 120^{\circ}=60^{\circ}\)

Step2: Identify the relationship between ∠2 and ∠3

∠2 and ∠3 are alternate - interior angles. When two parallel lines \(l\) and \(m\) are cut by a transversal \(t\), alternate - interior angles are equal.
So \(m\angle3=m\angle2\)

Answer:

\(60^{\circ}\)