Question

two parallel lines, ab and cd, are cut by a transversal as shown in the figure. if m
∠4 = 125°, which of the following is true?

m∠3 = 125°
m∠8 = 125°
m∠7 = 125°
m∠6 = 125°

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. \(\angle4\) and \(\angle2\) are vertical angles, so \(m\angle2=m\angle4 = 125^{\circ}\).

Step2: Use the property of alternate - exterior angles

Since \(AB\parallel CD\), alternate - exterior angles are equal. \(\angle2\) and \(\angle8\) are alternate - exterior angles. So \(m\angle8=m\angle2\).

Step3: Get the final result

Substitute \(m\angle2 = 125^{\circ}\) into \(m\angle8=m\angle2\), we get \(m\angle8 = 125^{\circ}\).

Answer:

\(m\angle8 = 125^{\circ}\)