Question

question 2 1 pts if ( mangle8 ) is ( 30^{circ} ), what is the measure of ( mangle4 )?

Explanation:

Step1: Find the measure of ∠2

When two lines intersect, vertical angles are equal. Since ∠8 and ∠2 are vertical angles, \(m\angle2 = m\angle8\). Given \(m\angle8 = 30^{\circ}\), so \(m\angle2=30^{\circ}\).

Step2: Use the property of parallel lines (if \(l\parallel m\))

If \(l\parallel m\) and \(t\) is a transversal, then ∠2 and ∠4 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(m\angle4=m\angle2\).

Answer:

\(30^{\circ}\)