Question

8.
←──────────────→
(3x - 70)° m∠2
←──────────────→
m∠1 (x + 30)°
m∠2 = ____________

Explanation:

Step1: Identify Angle Relationship

The two lines are parallel, and the transversal creates alternate interior angles (or corresponding, here they are equal). So \(3x - 70 = x + 30\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(2x - 70 = 30\). Add 70 to both sides: \(2x = 100\). Divide by 2: \(x = 50\).

Step3: Calculate \(m\angle2\)

Substitute \(x = 50\) into \(3x - 70\): \(3(50) - 70 = 150 - 70 = 80\).

Answer:

\(80^\circ\)