Question

if line m || line n and ∠2 measures 35°, what is the measure of ∠5? diagram of 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: 145°, 55°, 155°, 180°

Explanation:

Step1: Identify relationship between ∠2 and ∠6

Since line \( m \parallel \) line \( n \), and the transversal cuts them, \( \angle 2 \) and \( \angle 6 \) are corresponding angles. So \( \angle 6=\angle 2 = 35^\circ \).

Step2: Find ∠5 using linear pair

\( \angle 5 \) and \( \angle 6 \) form a linear pair, so their sum is \( 180^\circ \). Thus, \( \angle 5 = 180^\circ-\angle 6 \).
Substitute \( \angle 6 = 35^\circ \): \( \angle 5=180^\circ - 35^\circ=145^\circ \).

Answer:

\( 145^\circ \) (corresponding to the option "145°")