Question

the fence uses vertical posts l, m, and o to hold parallel rails n and p together. if ( mangle1 = 94^{circ} ), what is ( mangle16 )?
a. ( 76^{circ} )
b. ( 86^{circ} )
c. ( 90^{circ} )
d. ( 94^{circ} )

Explanation:

Step1: Find the measure of ∠2

Since ∠1 and ∠2 are supplementary angles (they form a linear pair), we know that \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle1 = 94^{\circ}\), then \(m\angle2=180^{\circ}-94^{\circ}=86^{\circ}\).

Step2: Use the property of parallel lines

Because rails \(n\) and \(p\) are parallel and posts \(l\), \(m\), \(o\) are transversals. ∠2 and ∠16 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So \(m\angle16 = m\angle2\).

Answer:

B. \(86^{\circ}\)