Question

parallel lines and transversals | find the... what is the measure of ∠2? multiple - choice question 90 50 180 70

Explanation:

Step1: Analyze given angle - sum equation

We know that \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\).

Step2: Find \(m\angle1\)

From the work shown, \(m\angle1 + 120^{\circ}=180^{\circ}\), so \(m\angle1=180 - 120=60^{\circ}\).

Step3: Find \(m\angle3\)

We have \(m\angle3+110^{\circ}=180^{\circ}\), so \(m\angle3 = 180 - 110=70^{\circ}\).

Step4: Calculate \(m\angle2\)

Substitute \(m\angle1 = 60^{\circ}\) and \(m\angle3 = 70^{\circ}\) into \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\). Then \(60^{\circ}+m\angle2 + 70^{\circ}=180^{\circ}\), so \(m\angle2=180-(60 + 70)=50^{\circ}\).

Answer:

50