Question

if line m || line n and ∠2 measures 47°, what is the measure of ∠5? diagram: two parallel lines m (top) and n (bottom) cut by a transversal, with angles labeled 1,2,3,4 (at intersection with m) and 5,6,7,8 (at intersection with n). below the diagram: multiple-choice options: 133°, 180°, 47°, 43°

Explanation:

Step1: Identify angle relationships

Since line \( m \parallel \) line \( n \), and the transversal creates angles. \( \angle 2 \) and \( \angle 6 \) are corresponding angles (so \( \angle 6 = \angle 2 = 47^\circ \)). Then, \( \angle 5 \) and \( \angle 6 \) are supplementary (they form a linear pair), so \( \angle 5 + \angle 6 = 180^\circ \).

Step2: Calculate \( \angle 5 \)

Substitute \( \angle 6 = 47^\circ \) into the supplementary angle formula: \( \angle 5 = 180^\circ - 47^\circ = 133^\circ \).

Answer:

\( 133^\circ \) (corresponding to the option "133°")