Question

lines are cut b
s 125°, then m∠5 is (s) 60°
ternate interior angles are (u) congruent
if m∠3 is 60°, then m∠6 is
if m∠3 is 60°, then m∠8 is (s) 120°
when two lines in a plane are cut by a transversal, and if corresponding
congruent, then the two lines are (f) intersecting

Explanation:

Step1: Identify Angle Relationships

Assume lines are parallel (from context: "when two lines in a plane..."). ∠3 and ∠8: ∠3 and ∠6 are supplementary (linear pair), ∠6 and ∠8 are congruent (alternate interior? Wait, ∠3 and ∠8: if ∠3 = 60°, ∠3 and ∠8: ∠3 + ∠8 = 180°? No, wait, ∠3 and ∠6 are supplementary (180 - 60 = 120°), ∠6 and ∠8: if parallel, ∠6 and ∠8 are... Wait, the problem says "If \( m\angle 3 = 60^\circ \), then \( m\angle 8 \) is". Let's recall: ∠3 and ∠5 are alternate interior (congruent), ∠3 and ∠6: same - side interior (supplementary), ∠3 and ∠8: ∠3 and ∠8: ∠3 and ∠6 are supplementary (\( m\angle 6 = 180 - 60 = 120^\circ \)), and ∠6 and ∠8 are vertical? No, ∠6 and ∠8: if ∠6 and ∠8 are... Wait, the marked answer is 120°, so let's check: ∠3 and ∠6 are same - side interior angles (supplementary), so \( m\angle 6 = 180 - 60 = 120^\circ \). Then ∠6 and ∠8: if they are vertical angles? No, ∠6 and ∠8: maybe ∠6 and ∠8 are congruent as alternate exterior? Wait, the key is that if two lines are parallel, same - side interior angles are supplementary. ∠3 and ∠6 are same - side interior, so \( m\angle 6 = 120^\circ \), and ∠6 and ∠8 are congruent (maybe corresponding or alternate). So \( m\angle 8 = 120^\circ \).

Step2: Confirm with the Marked Answer

The marked answer for \( m\angle 8 \) is (S) \( 120^\circ \), which matches the calculation using supplementary angles (since \( m\angle 3 = 60^\circ \), \( m\angle 6 = 180 - 60 = 120^\circ \), and \( m\angle 8 = m\angle 6 \) by angle relationships like vertical or alternate).

Answer:

For \( m\angle 8 \) when \( m\angle 3 = 60^\circ \) (assuming parallel lines), the measure is \( 120^\circ \) (option (S) \( 120^\circ \)).