Question

1. a fence on a hill uses vertical posts l and m to hold parallel rails n and p. if m\\(\angle1 = 115\\), then what is the measure of \\(\angle16\\)?

Explanation:

Step1: Find the measure of ∠2

Since ∠1 and ∠2 are supplementary (they form a linear pair), we use the formula \(m\angle1 + m\angle2=180^{\circ}\).
Given \(m\angle1 = 115^{\circ}\), then \(m\angle2=180 - 115=65^{\circ}\).

Step2: Use the property of parallel lines

Rails \(N\) and \(P\) are parallel, and posts \(L\) and \(M\) are transversals. ∠2 and ∠16 are corresponding angles.
By the Corresponding Angles Theorem (if two parallel lines are cut by a transversal, then corresponding angles are congruent), \(m\angle16=m\angle2\).

Answer:

\(65^{\circ}\)